Question

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.

Answer 1

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. 

Answer 2

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