Kabir wants to know the volume of a solid right pyramid with a square base. He uses a ruler to measure the length of the base as 8 inches. He then measures the slant height to be 5 inches.

The hypotenuse of the right triangle used to determine the height is

5 inches

The leg of the right triangle that lies on the same plane as the base is

4 inches

The height of the pyramid is

3 inches

The volume of the solid pyramid is

64 cubic inches

The volume of a pyramid is one-third of the product of its altitude and area of the base.

Area of the base = (8 in) ² = 64 in²

Altitude:

The altitude is the length of the right triangle formed from the base and the slant height as the hypotenuse.

(5 in) ² = h² + (4 in) ²

h = 3 in

Volume:

V = Ah/3

V = (64 in²) (9 in) / 3 = 192 in³

The volume of the solid right pyramid is equal to 192 in³.