An architect builds a $7$ ft tall square base pyramid. If $525$ cubic ft of sand can completely fill the pyramid, what is the side length of the base of the pyramid?

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Solution

Volume of the pyramid $=$ Volume of the sand $= 525$ cu ft

$\frac{1}{3} \times$ Area of the base $\times$ Height $= 525$

$\frac{1}{3} \times$ Area of the base $\times 7 = 525$

Area of the base $= \frac{525 \times 3}{7} = 75 \times 3 = 225$ sq ft

Let $“ s ”$ be the side length of the square base of the pyramid.
Then,
$s \times s = 225$
$s \times s = 15 \times 15$
$s = 15$ ft
Thus, the side length of the base of this pyramid is $15$ ft.

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An architect builds a 7 ft tall square base pyramid. If 525 cubic ft of sand can completely fill the pyramid, what is the side length of the base of the pyramid?

An architect builds a $7$ ft tall square base pyramid. If $525$ cubic ft of sand can completely fill the pyramid, what is the side length of the base of the pyramid?