The base of a cylinder has an area of 64π in2. If the height of the cylinder is 10 in., what is the total volume?

V = 3217.0 m3

Step-by-step explanation:

The base area is given and the height is equal to twice the radius.

Use the formula for the area of a circle to solve for the radius of the cylinder.

A=πr2

Substitute 64π for A.

64π=πr2

Divide both sides by π.

64=r2

Take the positive square root of both sides.

8=r

Therefore, the radius is equal to 8 m.

The height is equal to twice the radius.

h=2r

Substitute 8 for r.

h=2⋅8

Simplify.

h=16

Therefore, the height is equal to 16 m.

To find the volume of the cylinder, use the formula for the volume of a cylinder, V=πr2h.

Substitute 8 for r and 16 for h.

V=π⋅82⋅16

Simplify.

V=1024π

Use a calculator to approximate.

V≈3217.0 m3

Therefore, the volume of the cylinder is approximately 3217.0 m3.

see explanation

Step-by-step explanation:

The volume (V) of a cylinder is

V = area of base * height

here area of base = 64π and height = 10, hence

V = 64π * 10 = 640π in³ ← exact value