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.