Question

The diameter and height of this cylinder are equal to the side length, S, of the cube in which the cylinder is inscribed. What is the expression for the cylinder's volume?

Answer 1

V=hpir^2
d/2=r
d=h=s

s/2=r
V=spi(s/2)^2
V=$\frac{s^3pi}{4}$

Answer 2

Volume of a cylinder:
V = r² π h
r = S/2,  h = S
V = ( S/2 )² · π · S  = S²/4 · π · S = 1/4 π S³ 
Answer: A )