Question

*100 points* What is the maximum volume of a square pryamid that can fit inside a cube with a side length of 24 cm? A) 2,304 cm3 B) 4,608 cm C) 6,912cm3 D) 13,824 cm3s

Answer 1

4,608

Explanation:

The base of the pyramid is the same base as the cube, so base of pyramid is 24*24=576

The heights of the pyramid and cube would also be the same.

The base times the height is 576*24=13,824

Finally, to find the volume of the pyramid, you must multiply 13,824*1/3=4,608

Answer 2

B) 4,608.

Explanation:

A square pyramid with the maximum volume that can fit inside a cube has a same base as a cube ( 24 cm x 24 cm ) . The height of the pyramid is also same as a side length of a cube ( h = 24 cm ).

The volume of the pyramid:

V = 1/3 · 24² · 24 = 1/3 · 576 · 24 = 4,608 cm³

Answer:

The maximum volume of the pyramid is 4,608 cm³.