Question

Find the exact volume of the cylinder.

A) 80π ft^3
B) 160πft^3
C) 200πft^3
D) 400πft^3

Answer 1

`\boxed {\boxed {\sf C. \ 200 \pi \ ft^3}}`

Explanation:

We are asked to find the volume of the cylinder. The formula for calculating a cylinder's volume is:

`v= \pi r^2 h`

We know the height of the cylinder is 8 feet. We are given the diameter, the distance from edge to edge through the center. We want to find the radius, the distance from the edge to the center.

The radius is half the diameter.

• r = d/2
• r= 10 ft/2
• r=5 ft

We know both variables (h= 8ft and r=5 ft) and can substitute them into the formula.

`v= \pi (5 \ ft)^2 * (8 \ ft)`

Solve the exponent.

• 5 ft * 5ft = 25 ft²

`v= \pi (25 \ ft^2)(8 \ft)`

Multiply the numbers in parentheses.

`v= \pi (200 \ ft^3)`

`v= 200 \pi \ ft^3`

The volume of the cylinder is 200π cubic feet and choice C is correct.