Answer:
Three times
Step-by-step explanation:
Given
Figures: Rectangular Prism and Rectangular Pyramid
Let the dimension of the prism be:
[tex]l = length[/tex]
[tex]w = width[/tex]
[tex]h = height[/tex]
Amount of sand used is the volume (V1) and it is calculated using;
[tex]V_1 = l * w * h[/tex]
[tex]V_1 = lw h[/tex]
Since the pyramid has the same base area and height as the prism, the its dimension would be:
[tex]l = length[/tex]
[tex]w = width[/tex]
[tex]h = height[/tex]
Amount of sand used is the volume (V2) and it is calculated using;
[tex]V_2 = \frac{1}{3}*(lwh)[/tex]
So, we have:
[tex]V_1 = lw h[/tex]
[tex]V_2 = \frac{1}{3}*(lwh)[/tex]
Substitute lwh for V1 in the second equation
[tex]V_2 = \frac{1}{3}V_1[/tex]
Multiply both sides by 3
[tex]3 * V_2 = \frac{1}{3}V_1 * 3[/tex]
[tex]3 * V_2 = V_1[/tex]
Reorder
[tex]V_1 = 3 * V_2[/tex]
[tex]V_1 = 3 V_2[/tex]
Hence, the amount of sand used in building the prism is three times the amount of sand used in building the pyramid
