Question

Hi. I need help with this algebra question.

Use the equation v=pi r^2h to write a function v(x) for the volume of liquid a glass can hold. Let v(x)=140pi. Outer radius=x Outer height=4x . The thickness of the sides and bottom are 1cm. The glass is to hold 140pi cm^3.

Answer 1

I'm trying to help someone understand this. It's been over 18 years since I have had Algebra and I actually can't figure this out.

Answer 2

Do you just need a formula like v(x) = ???
Or are you trying to find the dimensions of the glass?

Answer 3

I just need the formula to start. I believe that the dimensions would be
Inner cylinder r= x-1 h= 4(x-1)
Outer cylinder r=x h=4(x)

Please correct me if I am wrong.

Answer 4

I think inner cylinder 4 = x - 2 (because there is thickness on both sides of the "circle"

Outer cyclinder h = 4x - 1 if the height was 20 with with thickness it would be 19.

Answer 5

OOPS you are correct... inner is x - 1 I was thinking diameter

Answer 6

I do think the height is 4x - 1

Answer 7

Good to know I was right on that part, lol. Can you help me out with the rewriting the equation in standard form? Thanks!

Answer 8

Sure... Are you thinking v(x) =pi (x-1)^2(4x-1).

I am not sure what they want with the 140pi

Answer 9

(x - 1)^2 = (x - 1)(x - 1) by foiling you get x^2 - x - x + 1 = x^2 -2x + 1

Then (x^2 - 2x + 1)(4x - 1) by distributing the 4x and then the - 1 you get
4x^3 - 8x^2 + 4x - x^2 + 2x - 1 then add like terms
4x^3 - 9x^2 + 6x - 1
pi(4x^3 - 9x^2 + 6x - 1)

Is this what you are looking for?

Answer 10

Yes that's what I was thinking. Here is the wording of the opening statement:

You are designing a cylindrical, plastic glass with an outside layer of water that, when frozen, keeps the contents of the glass cold. The outer height of the glass should be four times its outer radius, and the thickness of the sides and teh bottom of the glass should be 1 cm. The glass is to hold 140\[\pi\] cubic of liquid.

Answer 11

I think you are looking for an answer to the size of the glass.

140pi = pi(4x^3-9x^2+6x - 1 dividing both sides by pi

140 = 4x^3 - 9x^2 + 6x - 1 subtract 140 from both sides

0 = 4x^3 - 9x^2 + 6x -141

Do they let you use a calculator to solve this?

Answer 12

Yes. As a matter of fact, the next question lets them use it to use the zero (root) function to approximate the outer radius.

Answer 13

Good.. Put that in you calculator and find the positive root.

Answer 14

Thank you so much for your help. It's good to know that I was on the right path. I was uncertain where I was heading though, lol. Take care!

Answer 15

U R Welcome