Question

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?

Answer 1

Calculation of the volume of the pyramid will require us to use the equation,

V = Bh/3

where B is the area of the base and h is the height (right).

Assuming that the base is a square such that its area is equal to the square of the base edge measurement.

B = (10 cm)² = 100 cm²

Given that the base edge is 10 and the slant height is 13, the vertical height is equal to 12 cm.

The volume is therefore,

V = (100 cm²)(12 cm) / 3 = 400 cm³

Therefore, the aluminum available is still enough.