Answer:
Option C is correct
[tex]384 \pi[/tex] cubic inches
Step-by-step explanation:
Volume of cylinder(V) is given by:
[tex]V = \pi r^2h[/tex] ......[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=[tex]16 \pi"[/tex]
Since:
Base with Circumference(B) = [tex]2 \pi r[/tex]
[tex]16 \pi =2 \pi r[/tex]
⇒[tex]16 = 2r[/tex]
or
[tex]2r =16[/tex]
Divide both sides by 2 we have;
⇒[tex]r = 8''[/tex]
Substitute the given values in [1] we have;
[tex]V = \pi \cdot 8^2 \cdot 6 = \pi \cdot 64 \cdot 6[/tex]
Simplify:
[tex]V = 384 \pi[/tex] cubic inches
Therefore, the volume of a cylinder is, [tex]384 \pi[/tex] cubic inches
