Question

Max built a rectangular Prism and a rectangular Pyramid using beach sand. The prism and the pyramid have the same base area and the same height. The amount of sand Max used to build the Prism is how many times the amount used to build the Pyramid?

Answer 1

Three times

Explanation:

Given

Figures: Rectangular Prism and Rectangular Pyramid

Let the dimension of the prism be:

`l = length`

`w = width`

`h = height`

Amount of sand used is the volume (V1) and it is calculated using;

`V_1 = l * w * h`

`V_1 = lw h`

Since the pyramid has the same base area and height as the prism, the its dimension would be:

`l = length`

`w = width`

`h = height`

Amount of sand used is the volume (V2) and it is calculated using;

`V_2 = (1)/(3)*(lwh)`

So, we have:

`V_1 = lw h`

`V_2 = (1)/(3)*(lwh)`

Substitute lwh for V1 in the second equation

`V_2 = (1)/(3)V_1`

Multiply both sides by 3

`3 * V_2 = (1)/(3)V_1 * 3`

`3 * V_2 = V_1`

Reorder

`V_1 = 3 * V_2`

`V_1 = 3 V_2`

Hence, the amount of sand used in building the prism is three times the amount of sand used in building the pyramid