A cube is enclosed in a cylinder, what is the largest possible volume of the cube?

(1) The volume of the cylinder is 100π
(2) The area of the base of the cylinder is 25π
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We are given that a cube is enclosed in a cylinder nd we need to find out the maximum possible volume of the cube.
The volume of the cube depends on the side of the cube i.e volume = (side)^3 and the side of the cube and enclosure of the cube will depend on the radius and height of the cylinder.


Statement 1: Volume of cylinder = 100\(\pi\)
\(\pi\)\(r^2\)h=100\(\pi\)
r and h unknowkn
so statement 1 is insufficient

Now Statement 2: Area of base of cylinder =25pie
area of base = pie*r^2
so pie*r^2=25 pie
r^2=25
so r=5 (as r cannot be -5)
But we don't know the height of the cylinder
so Statement 2 is not sufficient

Combining both statement 1 and statement 2 we get r and h so we can know the largest possible volume of cube.
Hence the answer is Option C

The largest cube inside a cylinder depends on the latter's base radius and height.
Knowing just the base radius or just the height value of the cylinder is insufficient to determine the volume of the cube.

a) \(\pi r^2 h = 100 \pi\)
Both r and h are unknown. NOT SUFFICIENT

b)\(\pi r^2 = 25 \pi\)
r value is known. But we do not know anything about h. h may be smaller than r\(\sqrt{2}\). Therefore NOT SUFFICIENT.

Combining both a and b, we can know r and h and hence the value of the volume of the cube.
So answer is C