What is the volume of a square pyramid with base edges of 24 cm and a slant height of 37 cm?

7104
20160
10080
6720

1 answer

The correct answer is 10080 cubic cm.

To find the volume of a pyramid, we use the formula V = (1/3)Bh, where B is the area of the base and h is the height of the pyramid.

In this case, the base is a square with edges of 24 cm, so the area of the base is 24^2 = 576 sq cm.

To find the height of the pyramid, we can use the Pythagorean theorem. The slant height is the hypotenuse of a right triangle with legs of 24/2 = 12 cm (half the base edge) and h (the height we want to find).

37^2 = 12^2 + h^2
1369 = 144 + h^2
h^2 = 1225
h = 35 cm

Now we can plug in our values into the formula:

V = (1/3)(576)(35)
V = 10080 cubic cm