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# A right pyramid has a square base with area 288 square cm

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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?

Nov 8, 2020

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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?

Hello Guest!

$$a=\sqrt{288cm^2}\\ a=16.97cm\\ \frac{d}{2}=\frac{a}{2}\sqrt{2}=12cm\\ h=\sqrt{s^2-(\frac{d}{2})^2}\\ h=\sqrt{18^2-12^2}\\$$

$$h=13.416cm$$

$$V=\frac{1}{3}\cdot a^2\cdot h\\ V=\frac{1}{3}\cdot 288cm^2\cdot \sqrt{18^2-12^2}\cdot cm$$

$$V=1287.975\ cm^3$$

!

Nov 8, 2020