aeon86 wrote:

for the cube to be the largest possible, the diameter of the base has to be equal to the diagonal of one of the sides of the cylinder.

this makes it so that looked at from the top you would see a circumscribed circle around a square.

in order to know the volume of the cylinder you need to know the height of the cylinder and the radius or diameter of the base of the cylinder (or be able to determine them)

(1) The area of the base of the cylinder is 8π.

we can calculate the radius, but we know nothing about the height

Not suff

(2) x is 64

if the total volum of the square is 64 that makes the sides 4 and that would allow us to calculate the diameter or radius from there but again nothing is mentioned about the height

both together, we still don't know anything about the height:

E

A cube has all sides equal.

therefore, if volume is x, then base=length=height=x^(1/3)

and height of cylinder = height of cube = x^(1/3)

Now diameter of cylinder = diagonal of cube = sqrt[ L*L + B*B ] = sqrt[ x^(2/3) + x^(2/3) ]

Thus, Radius = sqrt[ x^(2/3) + x^(2/3) ] / 2

Area of base of cylinder = pi* r*r = [ pi *x^(2/3)*2 ] / 4 ------- EQ. A

volume of cylinder = area of base * height of cylinder = [ pi* x^(2/3)*x^(1/3) ] / 2 = [ pi*x ]/2

So we just need to find the value of x =?

Stmt 1 - we can calculate x from EQ A. we get x=64.

Stmt 2 - we are given x = 64

So volume = pi *(64/2) = 32*pi.

Hence, both the statements are sufficient individually. Correct answer is D.