+4609 A right pyramid has a square base with area 288 square cm. Its peak is 15 cm from each of the other vertices. What is the volume of the pyramid, in cubic centimeters?
+9466 I also get 864 cm3 (but exactly) 
area of square base = 288 so side length of base = √288
Let x be the diagonal of the base.
Let h be the height of the pyramid.
By the Pythagorean theorem....
(√288)2 + (√288)2 = x2
288 + 288 = x2
576 = x2
x = √576
x = 24
Again by the Pythagorean theorem...
(x/2)2 + h2 = 152
(24/2)2 + h2 = 152
144 + h2 = 225
h2 = 81
h = 9
volume of pyramid = (1/3)(area of base)(height)
volume of pyramid = (1/3)(288)(9)
volume of pyramid = 864 cm3
OK, I will take a crack at it! Let me know if I s***w up!!
Sqrt(288) = 16.97 cm - side length of the square base
By Pythagoras' theorem:
Slant Height =sqrt[15^2 - (16.97/2)^2]
Slant Height =12.3695 cm
Height =sqrt[12.3695^2 - 8.485^2]
Height =9 cm
Volume = 1/3 x H x Side Length^2
Volume = 1/3 x 9 x 16.97^2
Volume =~864 cm^3
+9466 I also get 864 cm3 (but exactly)
area of square base = 288 so side length of base = √288
Let x be the diagonal of the base.
Let h be the height of the pyramid.
By the Pythagorean theorem....
(√288)2 + (√288)2 = x2
288 + 288 = x2
576 = x2
x = √576
x = 24
Again by the Pythagorean theorem...
(x/2)2 + h2 = 152
(24/2)2 + h2 = 152
144 + h2 = 225
h2 = 81
h = 9
volume of pyramid = (1/3)(area of base)(height)
volume of pyramid = (1/3)(288)(9)
volume of pyramid = 864 cm3
