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?
+129852 Let's go through this
Slant height =18
The side of the base = sqrt (288) = 12sqrt 2
The diagonal length of the base = 12sqrt (2) * sqrt (2) = 24
Half of this diagonal length = 12
Using the Pythagorean Theorem, the height of the pyramid = sqrt [ slant height ^2 - (half of diagonal length)^2 ] =
sqrt [ 18^2 - 12^2 ] = sqrt (180) =6 sqrt (5)
The volume of the pyramid = (1/3) ( base area) (height) =
(1/3) (288) (6 sqrt (5) ) =
2 * 288 * sqrt (5) =
576sqrt (5) cm^3 ≈ 1287.975 cm^3 (just as qjin27 found !!!! )
