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?
+128475 The diagonal across the base = sqrt ( base area) * sqrt 2 = sqrt (288) * sqrt 2 = 12 sqrt 2* sqrt 2 = 24
1/ 2 of this = 12
18 is the slant height
The true height , h = sqrt [18^2 -12^2 ] = sqrt [ 324 - 144 ] = sqrt 180 = 6sqrt 5
The volume is
base area * height / 3 =
288 * 6 sqrt 5 / 3 =
288 * 3sqrt 5 cm^3 ≈ 1932 cm^3
