Question

Can someone help me plz

Answer 1

The side length of the square base is 18 inches and the height of the pyramid is 9 inches.

Step-by-step explanation:

Step 1:

The volume of a square pyramid is calculated by multiplying the square of the base edge with the height of the pyramid and $\frac{1}{3}$.

The volume of a square pyramid, $V = a^{2} \frac{h}{3}.$

Step 2:

From the given diagram, the base edge is the length of the four base edges which is x inches in this pyramid. a = x inches.

The height of the pyramid is from the base to the top, h = $\frac{x}{2}$ inches .

The volume of a square pyramid, $V = 972.$

Substituting the known values, we get

$972 = (x)^{2} (\frac{x}{2}) (\frac{1}{3} ) = \frac{x^{3} }{6} .$

$x^{3} = 6(972) = 5,832. x = \sqrt[3]{5,832} = 18.$

So x is 18 inches long.

The side length $= x = 18$ inches.

The height of the pyramid $= \frac{x}{2} = \frac{18}{2} = 9$ inches.