The base edge of a regular square pyramid measures 30 inches. The slant height of the pyramid measures 25 inches. Find the volume of the pyramid in terms of pi. I was having a lot of issues figuring this problem out, so if someone could explain it step by step that would be much appreciated! Thank you!
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The volume is (1/3)b²h, where b is the side of a base and h is the height. Since slant height is given, you'll have to use Pythagoras to find height. Draw a figure if you have to, and you'll see you can form a right triangle between the height (line from center of base to the top), half of the base, and the slant height. By Pythagoras:
(b/2)² + h² = s²
h = √(s² - (b/2)²)
h = √(25² - 15²)
h = √(625 - 225)
h = √(400) = 20
Then...
V = (1/3)b²h = (1/3)(30 in)²(20 in) = 6,000 in³
(b/2)² + h² = s²
h = √(s² - (b/2)²)
h = √(25² - 15²)
h = √(625 - 225)
h = √(400) = 20
Then...
V = (1/3)b²h = (1/3)(30 in)²(20 in) = 6,000 in³
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V = (1/3) Bh (1/3) (30 in)^2 (20 in) = (1/3) (900 in^2) (20 in) = 6000 in^3