Question

Find the volume of a cylinder of height 6" and base with circumference 16 pi". A.96 pi cubic units B.192 pi cubic units C.384 pi cubic units

Answer 1

The answer is C. 384 pi cubic units

Answer 2

Option C is correct

`384 \pi` cubic inches

Explanation:

Volume of cylinder(V) is given by:

`V = \pi r^2h` ......[1]

where,

r is the radius of the cylinder

h is the height of the cylinder respectively.

As per the statement:

Height of the cylinder(h) = 6"

Base with circumference=
`16 \pi`

Since:

Base with Circumference(B) =
`2 \pi r`

`16 \pi =2 \pi r`

⇒
`16 = 2r`

or

`2r =16`

Divide both sides by 2 we have;

⇒
`r = 8''`

Substitute the given values in [1] we have;

`V = \pi \cdot 8^2 \cdot 6 = \pi \cdot 64 \cdot 6`

Simplify:

`V = 384 \pi` cubic inches

Therefore, the volume of a cylinder is,
`384 \pi` cubic inches