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Olin [163]
3 years ago
12

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?
Mathematics
1 answer:
vova2212 [387]3 years ago
3 0

Answer:

Three times

Step-by-step 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 = \frac{1}{3}*(lwh)

So, we have:

V_1 = lw h

V_2 = \frac{1}{3}*(lwh)

Substitute lwh for V1 in the second equation

V_2 = \frac{1}{3}V_1

Multiply both sides by 3

3 * V_2 = \frac{1}{3}V_1 * 3

3 * V_2 = V_1

Reorder

V_1 = 3 * V_2

V_1 = 3 V_2

<em>Hence, the amount of sand used in building the prism is three times the amount of sand used in building the pyramid</em>

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