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iogann1982 [59]
3 years ago
12

Can someone help me plz

Mathematics
1 answer:
viva [34]3 years ago
4 0

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.

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