A right pyramid has a square base with area 288 square cm. Its peak is 18 cm from each of the other vertices. What is the volume of the pyramid, in cubic centimeters?
+14915 A right pyramid has a square base with area 288 square cm. Its peak is 18 cm from each of the other vertices. What is the volume of the pyramid, in cubic centimeters?
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\(a=\sqrt{288cm^2}\\ a=16.97cm\\ \frac{d}{2}=\frac{a}{2}\sqrt{2}=12cm\\ h=\sqrt{s^2-(\frac{d}{2})^2}\\ h=\sqrt{18^2-12^2}\\\)
\(h=13.416cm\)
\(V=\frac{1}{3}\cdot a^2\cdot h\\ V=\frac{1}{3}\cdot 288cm^2\cdot \sqrt{18^2-12^2}\cdot cm\)
\(V=1287.975\ cm^3\)
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