Question

A right pyramid with a square base is shown.
There is 1,000 cm3 of aluminum available to cast a trophy that will be in the shape of a right square pyramid. Is this enough aluminum for a trophy that has a base edge of 10 cm and a slant height of 13 cm?

No, the volume of the trophy is 1,200 cm3.
No, the volume of the trophy is 1,300 cm3.
Yes, the volume of the trophy is 400 cm3.
Yes, the volume of the trophy is 433.333 cm3.

Answer 1

Yes. Base area = 10^2 = 100 cm^2. Slant height l = 13 and half the base = 5, so height h = sqrt(13^2 − 5^2) = sqrt(169 − 25) = 12 cm. Volume = (1/3)(base area)(height) = (1/3)(100)(12) = 400 cm^3.