Question

A square pyramid is inscribed in a cube of total surface area of $24$ square cm such that the base of the pyramid is the same as the base of the cube. What is the volume of the pyramid?

• A. $\frac{1}{3}$
• B. $\frac{8}{3}$
• C. $6$
• D. $4$
• E. $8$

Answer 1

The correct option is B $\frac{8}{3}$

Given that total surface area of cube is $24$ and cube has $6$ faces. so the area of each face is $\frac{24}{6}=4$
therefore the length of side of each face and the height of cube is $2$
So the volume of pyramid is $\frac{lwh}{3}=2\times 2\times \frac{2}{3}=\frac{8}{3}$