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The height of the pyramid is 7cm and the base is 5 times the square root of pi. Find the volume of the pyramid.

User KGo
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Final answer:

The volume of the pyramid with a height of 7cm and a square base 5 times the square root of pi is ((175π) / 3) cm³ or approximately 183.26 cm³.

Step-by-step explanation:

To find the volume of the pyramid with a height of 7cm and a base where each side is 5 times the square root of pi, we can use the formula for the volume of a pyramid, which is V = (1/3)Ah, where A is the area of the base and h is the height of the pyramid.

First, we calculate the base area of the pyramid by squaring the length of a side of the square base, which is 5 times the square root of pi, or (5√π) cm. So, A = (5√π)^2 = 25π cm².

Next, we substitute the base area A and height h into the volume formula: V = (1/3) × 25π × 7 cm = (25π × 7 cm) / 3. This simplifies to V = (175π) / 3 cm³ or approximately V = 183.26 cm³ when pi is approximated as 3.1416.

User Unice
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