Question

What is the maximum volume of a square pyramid that can fit inside a cube with a side length of 12 cm?

A. 576
B. 288
C. 1,728
D. 864

All those are cm^3

Answer 1

The correct answer is option A. 576 cm^3

The volume of cube if side 12 cm = 12*12*12 cm^3
= 1728 cm^3
Now, volume of square pyramid =
`a^(2) (h)/(3)`

For maximum volume of square pyramid, a = h = 12 cm

Therefore, volume of square pyramid =
`( a^(3) )/(3)` = 1728/3 = 576cm^3