# Math

posted by .

How to setup this equation?

Find the ratio of the surface area of a cylinder to the volume of the cylinder if the height remains at 10 cm. Simplify this ratio and let f(x) = the simplified ratio. Let r be the radius of the cylinder.

a) Find the average rate of change as the radius increases from 2 to 5 cm.

Volume:πr^2
SA: 2π^2 + 2πrh

• Math -

Both of your formulas are incorrrect

Vol of cylinger = πr^2 h
SA = 2πr^2 + 2πrh

so when h = 10,
SA/V = (2πr^2 + 20πr)/(10πr^2
= (r + 10)/(5r)

f(r) = (r+10)/(5r)
f(2) = 12/10 = 6/5 = 1.2
f(5) = 15/25 = .6

avg rate of change = (.6-1.2)/(5-2) = -.2

## Similar Questions

1. ### Precalculus

How do you setup the equation for this? Thanky ou! Find the ratio of the surface area of a cylinder to the volume of the cylinder if the height remains at 10 cm. Simplify this ratio and let f(x) = the simplified ratio. Let r be the
2. ### Geometry Help & Proofs

The ratio of the volume of Cylinder A to the volume of Cylinder B is 1:5. Cylinder A is similar to Cylinder C with a scale factor of 1:2 and Cylinder B is similar to Cylinder D with a scale factor of 1:3. What is the ratio of the volume …
3. ### Algebra 1--How Am I Supposed to Solve This?!

Suppose a cone and a cylinder have the same radius and that the slant height l of the cone is the same as the height h of the cylinder. Find the ratio of the cone's surface area to the cylinder's surface area. Area of cone: S = πrl …

I do not want to fail this, could you please help me with number 1 and 3.D, and then check my other answers?
5. ### Math

1. Find and simplify the volume-to-surface-area ratio for each of the three possible ice cube shapes. You can use this chart. |Shape| S/A Formula|Volume Formula Cube | S.A=6s^2 | V=s^3 Sphere|S.A+4 pi r^2|V=4/3 pi r^3 Cylinder| S.A=2 …
6. ### Math

I am doing a project, are my answers correct?
7. ### maths

the ratio between the radius of the base and height of a cylinder is 2:3.if its volume is 1617.find the total surface area of cylinder
8. ### Math

Suppose Cylinder A has the same height but twice the radius of Cylinder B. What is the ratio of the volume of Cylinder B to Cylinder A?
9. ### mathmatic

find the volume to surface area ratio for a cylinder use 1.7 as the radius and 3 for the height show your calucations
10. ### Geometry

Cylinder A has a radius of 1m nad a height of 3m. Cylinder B has a rauis of height 3m. What is the ratio of the volume of cylinder A to the volume of cylinder B?

More Similar Questions