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

Question

asked Oct 8, 2018 196k views

2 Answers

Tim Copenhaver · Answer 1 · 2018-10-12T16:00:59+0000

Answer:

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