# The Task for Inverse functions is due on Monday, Feb. 25

The task posted on files in our course site is due on Monday, Feb. 25, and it should be discussed here. (I am attaching it here as well).

1. a) What are you asked to do in the first question a) in the task?                            b) Is there any formula that helps you to do that?                                                          c) What is known and what is unknown? Do you see any function ? If yes, specify the independent and the dependent variable and their relation in the function.
2. What are you asked to do in the second question b) in the task?                            Does the formula help you to find the height straight forward, or you see the inverse function?
3. In how many ways you can solve the question b from the task? Discuss. Think outside the box, bring any other ideas.

## 36 thoughts on “The Task for Inverse functions is due on Monday, Feb. 25”

1. Norbert Sziffer says:

when it comes to part a) we know the diameter and height of the cylinder. To know if we have enough material we have to find the volume of the cylinder
d = 6.985 cm
h = 0.381 cm
V=h*pi*r^2= 14.6cm^3, having the 30cm^3 of steel that means they have enough material for the piece.
b) f(30)=14.6x
by finding solution to this equation we going to know by how much the height can be be incresed
x=2.05 that means they can double the height of cylinder

2. jose rodriguez says:

1A) In the first task of the individual work it is asking us to figure out if Professor smith has enough material to cover the solid that he printed with the dimensions given.
1B) Since Professor Smith printed the part the shows as a cylinder we can use the Formula V=pi(r)^2(h).
If we plug in what we know into the Formula it would be V=pi(34.925mm)^2(3.81mm)= 14599.83mm ~ 14.6 cm
1C) First we know that Height = 3.81mm, the Diameter 69.85mm, and he has 30 steel.
2) In part B we are asked what would the height be if he was to use all the material he has on hand.
Since he has 30 steel the material would be enough to cover it and if he wanted to increase the height he can actually double the height since 14.6 cm can go into 30 a little bit more then 2 times
3)Another way can possibly be to double the volume, keep the radius and then find H.

1. Lucie Mingla says:

Hi Jose,
Please work properly with the units. Do no forget mm and mm^3 are not the same. Also, you need to show the converting from mm^3 to cm^3.

3. Kennethm says:

1a) In the first question of the task we are asked to find the volume of the cylinder and see if it is more or less than 30cm^3

1b) the formula to help me with this is the volume formula (V=h*pi*r^2)

1c) the height and diameter is known is mm. We have to convert it to cm and find the unknown radius from the diameter. The function could be the volume formula. The independent is h*pi*r^2 and the dependent is V

2) In B we are asked if we wanted to use all the steel what would the height of the cylinder be. Here I didn’t use the formula since I knew the volume of the original was 15cm^3 (0.391*pi*3.4925^2=14.98302346 rounded to 15) and I knew I could only raise the height to try to use all 30cm^3 I just doubled the height from 0.391 to 0.782 since 15*2 is 30.

3) You could solve it in 2 ways that I see. One is to do what I did which was more common sense but another way could be the inverse of the volume formula if the numbers didn’t fit so well.

4. RyanRamroop says:

1.a) To begin, we understand that we must find the volume of the cylinder, given the height, h= 3.81mm, and diameter, d=69.85mm. We must then convert to cm, since the volume of steel is in cm. With the given, we could utilize the formula for the volume of a cylinder, V=pi x r^2 x h. Using the equation we know that he does have enough steel to make the cylinder because the volume of the cylinder comes up to 14.59cm^3.
1.b) To increase the height of the cylinder to utilize all of the material, you could use the same formula but replace the total volume with 30cm^3(the total amount of steel) and solve for h, the height, while retaining pi and the diameter. **30cm^3=pi x 3.49^2 x h** Thus, he could increase the total height to 7.84 mm.

5. sufian says:

1A). In the first question, we are asked to find the volume to find out if he has enough material.
1B). The formula that will help me solve this is V=H*pi*r^2
1c) the things that are known are the height and diameter. What we have to find is the volume.
2) question B asked if we used all 30 steel what would the height be. By solving the volume formula I got an answer that was less than 15 so, it is possible to double the height because the total material he had was 30 and 15*2=30. which means the height is 3.81*2. so I didn’t need to use the inverse.
3) the first way you can solve this is by using the volume formula and then just multiplying the height times 2 and the second way is by using the inverse.

1. Lucie Mingla says:

Great point! In your method there was no need to use the inverse function. Please look at other students’s response to see how they used the inverse.

6. sufian says:

1A). In the first question, we are asked to find the volume to find out if he has enough material.
1B). The formula that will help me solve this is V=H*pi*r^2
1c) the things that are known are the height and diameter. What we have to find is the volume.
2) question B asked if we used all 30 steel what would the height be. By solving the volume formula I got an answer that was less than 15 so, it is possible to double the height because the total material he had was 30 and 15*2=30. which means the height is 3.81*2. so I didn’t need to use the inverse.
3) the first way you can solve this is by using the volume formula and then just multiplying the height times 2 and the second way is by using the inverse.

7. Khadra Shihadeh says:

1A)For the first question, we need to find if the material is enough to make the cylinder part of the piece the professor wants to print.
1B)The formula that could help with this is V= pi(r^2)h. I think this is the right formula because the professor has 30cm^3 of steel so the formula must make it so that the ending unit has cm^3. I do has some questions about this though because I’m having a hard time conceptualizing why it would be volume if its a hollow cylinder. If we use the formula we find that he has enough because the volume comes out to be 14.59cm^3.
1C)We have the diameter 69.85mm and the height 3.81mm. I do see a function because the thickness can change so depending on how that changes, the over all material needed would change, similar to input and output. The independent variable would be the measurements and the dependent variable could be the steel used ultimately.
2) a) for the second question we are asked what would the height be if were to use all of the material or steel. We could use inverse functions to plug in the volume and solve for the height, he would have to double the height, 7.62mm
3) You could reverse solve, or solve for the height by plugging in, or you could use inverse functions, but easiest of all is if you realize that just by doubling the height you would use up all the material.

1. Lucie Mingla says:

Great! You figured that you can just double the height to consume the whole material since the volume for the first one was 14.59 cm^3 and actually there is 30 cm^3 available as material.
I like the way(in point 3) you are twisting the idea of using the inverse to solve for h, but the easiest way is to double the height .

8. steve vargas says:

1a) Professor Smith whats to find out if he has enough material for the piece. Also if he want to increase the height of the piece and thickness what would it be.
1b) Since the part shows the cylinder i will be using the Formula V=pi(r)^2(h).
and if we plug in the numbers into the Formula it would be V=pi(34.925mm)^2(3.81mm)= 14599.83mm ~ 14.6 cm
1c) the knows are Height = 3.81mm, Diameter 69.85mm, and he has 30cm steel.
2)B ask us to use all the steel what would the height of the cylinder be. so i did 15cm^3 0.391*pi*3.4925^2=14.98302346
3)you can solve this 2 ways using the inverse (f(x)=…….) and (f^-1(y)=…..)

1. Lucie Mingla says:

What’s your max height for the 30 cm^3 amount of material?

9. Dillon Singh says:

A) In the first part, we are tasked to find the volume of the cylinder (that is how to find out how much material is needed). So, you use the volume formula for a cylinder: V =πr²h.

B) For the second part, we need to use what we are given to solve the problem. We know that the diameter is 69.85 mm. We also know that the height (thickness) is 3.81 mm. Again, the professor would like to know if he has enough material. (he has 30cm³) To solve this, you first need to convert the mm values to cm (69.85 mm = 6.985 cm) & (3.81 mm = 0.381 cm). After, you can plug the new cm values into the volume formula for a cylinder. *Remember* The radius is half the diameter. So, your radius for this problem would be: 3.4925. Once solved, I got 14.59cm³ as my answer. This means that the professor has more than enough material as he has 30cm³ to use. He can actually double the thickness if he wants.

10. Sadman Arefin says:

Question no 1.
The question is asking us to find is there enough materials to print the whole piece.
Given:
Professor Smith has 30cm^3 steel material. We also know the dimensions of the cylinder, which is
height = 0.381 cm
diameter = 6.985 cm
Dependent variables: volume
The formula that we will use is the volume formula, which is v=pi*r^2*h
=pi*(3.49cm)^2*(0.381 cm)
=14.58cm^3 (approximately 15 cm^3)
To print the whole piece Professor Smith will need 15 cm^3 material. He already has 30 cm^3 steel, which means he has enough materials to print the piece.
Question no – 2:
This question is asking that with all the materials he has, how much height can he increase of the piece.
In this case, we don’t need to use any formulas.
By using 15cm^3 materials, the height of the piece is 0.381 cm. So using 30cm^3 materials will double the height of the piece, the height will be approximately 0.762 cm.
Another way we can find the height is by setting it up to proportions.
(15cm^3/0.381cm)=(30cm^3/h)
h=0.762cm

11. Sadman Arefin says:

Question no 1.
The question is asking us to find is there enough materials to print the whole piece.
Given:
Professor Smith has 30cm^3 steel material. We also know the dimensions of the cylinder, which is
height = 0.381 cm
diameter = 6.985 cm
Dependent variables: volume
The formula that we will use is the volume formula, which is v=pi*r^2*h
=pi*(3.49cm)^2*(0.381 cm)
=14.58cm^3 (approximately 15 cm^3)
To print the whole piece Professor Smith will need 15 cm^3 material. He already has 30 cm^3 steel, which means he has enough materials to print the piece.
Question no – 2:
This question is asking that with all the materials he has, how much height can he increase of the piece.
In this case, we don’t need to use any formulas.
By using 15cm^3 materials, the height of the piece is 0.381 cm. So using 30cm^3 materials will double the height of the piece, the height will be approximately 0.762 cm.
Another way we can find the height is by setting it up to proportions.
(15cm^3/0.381cm)=(30cm^3/h)
h=0.762cm

12. Sadman Arefin says:

Question no 1.
The question is asking us to find is there enough materials to print the whole piece.
Given:
Professor Smith has 30cm^3 steel material. We also know the dimensions of the cylinder, which is
height = 0.381 cm
diameter = 6.985 cm
Dependent variables: volume
The formula that we will use is the volume formula, which is v=pi*r^2*h
=pi*(3.49cm)^2*(0.381 cm)
=14.58cm^3 (approximately 15 cm^3)
To print the whole piece Professor Smith will need 15 cm^3 material. He already has 30 cm^3 steel, which means he has enough materials to print the piece.
Question no – 2:
This question is asking that with all the materials he has, how much height can he increase of the piece.
In this case, we don’t need to use any formulas.
By using 15cm^3 materials, the height of the piece is 0.381 cm. So using 30cm^3 materials will double the height of the piece, the height will be approximately 0.762 cm.
Another way we can find the height is by setting it up to proportions.
(15cm^3/0.381cm)=(30cm^3/h)
h=0.762cm

13. Dane Deans says:

1)
a) The question asks us to find the volume of the cylinder and to see whether it is more or less than 30 cm^3.
b) I used the volume formula (V=h*pi*r^2).
c) The height and diameter is already known. The height is 3.81 mm and the diameter is 69.85 mm. With that information we have to find the volume.

2) B asks us to use all the steel and if so, what would the height of the cylinder be? So
I did 0.391*pi*3.4925^2=14.98302346 and rounded it to 15. After I just doubled the height and got 30.

3) You could solve it in 2 ways, one is by just doubling the height and the other way is the inverse function.

14. Rafaeldiaz2435 says:

1a) the first question is asking us to find if there are enough materials to print the entire piece

1b)the formula I used was V=pi*r^2*h

1c)H=3.81mm, D69.85mm, and 30cm^3 steel material

2) B wants to use all the steel to know the height of the cylinder so I used 15^3 0.391*pi*3.4925^2=14.9
rounded equals 15.
3) another way how to solve this is to use f^-1(y)

15. Rafaeldiaz2435 says:

1a) the first question is asking us to find if there are enough materials to print the entire piece

1b)the formula I used was V=pi*r^2*h

1c)H=3.81mm, D69.85mm, and 30cm^3 steel material

2) B wants to use all the steel to know the height of the cylinder so I used 15^3 0.391*pi*3.4925^2=14.9
rounded equals 15.
3) another way how to solve this is to use f^-1(y)

16. Eamon Bolger says:

1A) In the first question we are given the diameter and the height and asked to find the volume. We are also asked if he will have enough material to complete his piece when he has a total of 30 cm^3 of steel
1B) the formula that i found helpful in finding volume was V=H*PI*R^2 also know as the formula for the volume of a cylinder. Using this formula you can plug in V=(.381)(3.4925^2)(PI) which would equal to 14.6 cm^3 which could be rounded up to about 15 cm^3 leaving him with more than enough stock to make the piece
1C) What we know is that the diameter is 6.985 cm which means the radius is 3.4925 cm and we know that the height is .381 cm. We also know that the piece is a cylinder and he has 30 cm^3 of steel. what is unknown is the volume of the piece he is trying to make.
2) in this question we are being asked how thick can the piece be increased by using the remaining material? I determined that he can go slightly over double his original thickness, this is because he use about 15 cm^3 so if he doubled his thickness it would bring him up to about 30 cm^3.
3) I see two possible ways to solve for B, one is to use the volume of a cylinder formula then when you come to your answer double it and get the final height. The other way is to use the inverse of the function to get your answer although this way is a bit over complicated for a problem like this.

17. Anthony Leung says:

a) What are you asked to do in the first question?
I am being asked to find out if there are enough materials.
b) Is there any formula that helps you to do that?
V=pi*r^2*h
c) What is known and what is unknown?
Height=3.81 mm, Diameter= 69.85mm Whole thing=30cm^3 The given information allows me to find the volume.
Do you see any function ? If yes, specify the independent and the dependent variable and their relation in the function.
No I don’t see any functions.

What are you asked to do in the second question b) in the task?
The question is asking how much is needed to be added to increase the height. So you plug in the given into the formula( 15^3 0.391*pi*3.4925^2=14.9). The answer is approximately 15.

Another way of doing this is by using the other method from the article that you had us read.

1. Lucie Mingla says:

Well, you can see that the volume is directly proportional to the height and to the square of the radius. Considering the radius as constant (since we are not changing it) the volume is directly proportional to the height, and that is a function. V(h)= B* h (where B is the area of the base of cylinder)

2. Lucie Mingla says:

Well, you can see that the volume is directly proportional to the height and to the square of the radius. Considering the radius as constant (since we are not changing it) the volume is directly proportional to the height, and that is a function. V(h)= B* h (where B is the area of the base of cylinder)

18. Tamur Arshad says:

1a) In this question we are asked that does the professor has enough materials to print the whole piece.

b)The height needed in order to increase the thickness of the cylinder so the formula that would be applied is V=height*pi*r^2. ; 0.391*pi*3.4925^2=14.9.
To print the whole piece paper he approximately need 15 however he already got double the amount of it to print the piece.

19. Steven Meza Sanchez says:

1a) The problem is asking if there is enough material
1b) we can use the formula V=h*pi*r^2
1c) the known is the height= 3.81mm and dia= 69.85mm and 30cm^3 of steel
2a)we are asked if we wanted to use all the steel what would the height of the cylinder be
2b)the original volume is roughly 15cm^3, the professor has 30cm^3 so the height can be doubled
2c)one way to solve is just solve for height rearrange to formula to h= v/pi*r^2

20. Punnett says:

1a. We are tasked with finding out if Prof. Smith has enough material for the piece.
1b. The formula that can help us determine this is Volume = πr^2h
1c. We know that the height of the piece is 3.81mm, the diameter of the circle is 69.85mm.

2. In the second question we are asked to find out the height of the piece when he wants to use all the material he has at his disposal. The total height we would have is 7.62mm (.762cm^3) since the original is 3.81mm (.381cm^3)

3. You can also use F^-1(y) to solve for part b because it would be the inverse of the function.

21. ChadLam says:

1. a) The first question is asking if the Professor has enough material to 3d print his piece in steel.

b) The formula you can use to find the volume of the cylinder is V=pi*r^2*h.

c)What we know the height which is 3.81 mm (0.381 cm), the diameter which is 69.85 mm (6.985 cm), and the radius which is 34.925 mm (3.4925 cm). The independent is pi*r^2*h and the dependent is the volume.
v= pi*(3.5925)^2*(0.381)=14.5998 which is approximately 14.6 cm^3

2. In part B we are asked what the height would be if he used all the material.
He has enough material to increase the height as he has 30 cm^3 of steel and the amount he needed was 14.6 for the original piece. He has enough material to go double the original height as 14.6*2= 29.2 cm^3 this is less than 30 cm^3.

3. There are two ways to solve part b. One way is to double the volume and another way is to use the inverse function.

22. Michael Colon says:

1a. The first task asks us if the Professor has enough material to 3d print his piece out of steel.
1b. The formula we can use is the formula to find the volume of a cylinder (V = pi * r^2 * h )
1c. We know the height (3.81 mm) , the diameter (69.85 mm) and the amount of steel available (30cm^3)
The independent variable is the formula for the volume, the dependent variable is the total volume.

2. We are asked to find out the height of the piece when he wants to use all the steel he has available. The total height he would have for his piece would be doubled.

3. There are two different ways to solve part b. You can use the inverse function or simply double the volume.

23. Lucie Mingla says:

Can someone use the second method (solving for h), so the others can see it?

24. Abhijeet says:

In the first question it asks us to find if there’s enough space for the cylinder that professor smith created. And it also asks us for the height that it can increase. A formula we can use is v=h*pi*r^2.
B) In the second question it asks us too find out how much it the height professor smith can increase it by. For this question the formula is easier for me because for me it’s more straight forward and most of the values are given.
3) From question b I only thought about using one formula and that was v=h*pi*r^2. I substituted some of the values but for the radius, I had to divide the diameter by 2 to get the radius.And I converted every value given to cm because the cylinder steel value was given in cm.
So v=0.381*3.14159*3.4925^2
=14.59
=14.6 Cm^3
So professor smith can have enough material for the piece.
The other question I divided 30 cm^3 by 14.6 cm^3 and I got 2.05.And that’s how much the height can be increased.

25. Jose says:

1A. We need to find the volume of the cylinder and see if it is less than or more than 30cm^3

1B. The formula that I used was volume which is V=h*pi*r^2

1C. The diameter and height is in millimeters. We have to convert it into cm and find the radius from the diameter. The function could be the formula for the volume. The independent is h*pi*r^2 and the dependent is V

2. We are asked if we wanted to use all the steel what would the height of the cylinder be. The original volume is about 15cm^3 and the professor has 30cm^3. This shows that the height can be doubled

3) You can solve it by doubling the volume or by using the inverse function.

26. Randy Ramgoolam says:

1a) The first question asks us to find the volume in order to find out if he has enough material for the pieces.
1b) The formula that helps you find the volume is (V=pi*r^2*h)
1c) The things that are known is the height and diameter. In order to solve this question you first have to convert mm to cm. This helps you find the unknown radius from the diameter.
2) In part B we are asked what the height would equal if we use all the material. The formula does help you find the height straight forward but you can also use the inverse function. Based on the volume formula V=pi*(3.495)*(0.381) and this equals 14.6 and when you double it you get 29.2 therefore he has enough material to go double the height of the cylinder.
3) You can solve this problem in two ways. You can either use the volume formula or inverse function.

27. chrisllig10 says:

1a) The question is asking us if we have enough material
1b) the formula we use for this problem is V=h*pi*r^2
1c) the given is h=3.81mm and dia=69.85 mm and the we have 30cm^3 of steel
2a) in part b we are asked what the height would equal if we use all the material.
2b) the volume is about 15cm^3 meaning we can double the height
2c) use formula h=v/pi*r^2

28. Jruan says:

1a) The question is asking us if we have enough material to recreate the printing out of steel
1b) The formula used to solve this is to use the volume formula. V=(H * pi * R^2)
1c) The knowns are the Diameter and the Height of the cylinder. What we need to find is the volume of the cylinder to determine if we have enough material.
2) Question B asked if we can use only 30 steel to increase the height(thickness) of the piece. By using the volume formula the volume of the cylinder is rounded to 15 cm^3. ( V= (3.81 * pi * 34.925^2) Since the professor only has 30 steel, he could just double the height and see that 30 steel is roughly enough.
3) One way to solve this was to use the inverse function

29. Jruan says:

1a) The question is asking us if we have enough material to recreate the printing out of steel
1b) The formula used to solve this is to use the volume formula. V=(H * pi * R^2)
1c) The knowns are the Diameter and the Height of the cylinder. What we need to find is the volume of the cylinder to determine if we have enough material.
2) Question B asked if we can use only 30 steel to increase the height(thickness) of the piece. By using the volume formula the volume of the cylinder is rounded to 15 cm^3. ( V= (3.81 * pi * 34.925^2) Since the professor only has 30 steel, he could just double the height and see that 30 steel is roughly enough.
3) One way to solve this was to use the inverse function

30. Adrian Guin says:

a) In the first question of the problem, it is asking us if we have enough materials to be able to create the piece.
b)Yes, this formula is the one that helped me do the problem: “(V+pi*r^2*h)”
c)The known is the diameter of the circle and the height of the cylinder. and the unknown is the radius. Also, we have to convert millimeters into centimeters. The independent variable is the formula “(V+pi*r^2*h)” and the dependent is the volume.
d)In the second part of the problem, they are asking us that if we use all the materials what would be the new heigh of the piece. The formula will help us find it just if you plot the needed numbers to get a good new answer.
e) I think there are many ways to solve question b of the task but I truly think that you will always need this formula to be able to do it “(V+pi*r^2*h)”