Question

A triangular pyramid has a volume of 333 and one-third yards cubed. What are the possible measures of the area of the base, B, and the height, h, of the pyramid?

Answer 1

The correct answer is the possible measure of area of the base, B, and height of the pyramid, h, can be 3, 9, 111 or 37.

Explanation:

Volume of a triangular pyramid is 333
`(1)/(3)` cubic yards.

Volume of a triangular pyramid in general is
`(1)/(3)` × B × h where the area of the base is B, and the height is h.

Equating the volume we get,

`(1)/(3)` × B × h = 333
`(1)/(3)`

⇒ B × h = 333

⇒ B × h = 3 × 3 × 37

Thus the possible measures of area of base B and height of pyramid h are 3, 9, 37 or 111.