Question

The height of a cylinder is 4 millimeters. The circumference of its base is 10pi mm.

a. What is the radius of the cylinder? Explain.
b. Find the volume of the cylinder to the nearest tenth.

Answer 1

Solutions below.

Explanation:

Cylinder Formulas

Lets define the required formulas for the question regarding the cylinder.

The base of the cylinder is a circle, therefore the formula for the circumference of the base is:

`2\pi r`

The formula for the volume of the cylinder is:

`\pi r^(2) h`

Question

a) Given from the question, the circumference of the base is
`10\pi` mm.

Therefore, we can use the circumference formula to find radius of the base.

`2\pi r = 10\pi \\2r = 10\\r = (10)/(2) \\r = 5mm`

b) With all the parameters given, we can find the volume of the cylinder.

Volume of the Cylinder =

`\pi r^(2) h\\= \pi (5)^(2) (4)\\= 100\pi mm^(3) \\= 314.2mm^(3) (nearest\ tenth)`