Question

If a cube fits exactly in a cylinder with a height of h, then the volume of the cube is __________ and the surface area of the cube is __________.

• A. $h^3$
• B. $6h^2$

Answer 1

Step 1: Find the volume of the cube

Given, that the cube fits the cylinder exactly (break it into two step

So, side of the cube = height of the cylinder = $h$

The volume of the cube $=sid{e}^3=h^3$ ( $\because side=h$)

Step 2: Find the surface area of the cube

The surface area of the cube $=6sid{e}^2$ ( $\because side=h$)

$=6h^2$

Hence, the volume of the cube is $\underline{h^3}$ and the surface area is $\underline{6h^2}$.