Question

A square pyramid has a height of 6 units and a volume of 70 units. If a square prism has the same base area and volume as the square pyramid, what is its height?

a) 2 units
b) 4 units
c) 6 units
d) 8 units

Answer 1

a) 2 units. The height of the square prism is 2 units.

Step-by-step explanation:

To find the height of the square prism, we need to first determine the base area of the square pyramid. The volume of the square pyramid is given as 70 units, and the formula for the volume of a pyramid is 1/3 * base area * height. We can rearrange this formula to find the base area: base area = volume * 3 / height = 70 * 3 / 6 = 35 square units.

Since the square prism has the same base area, its base area is also 35 square units. To find the height of the prism, we can use the formula for volume of a prism: volume = base area * height. Rearranging this formula, we have height = volume / base area = 70 / 35 = 2 units.

Therefore, the height of the square prism is 2 units.