what volume of a square pyramid with base edges of 24 cm and a slant height of 37 cm?

a) 7104 cm^3
b) 20160 cm^3
c) 10080 cm^3
d) 6720 cm^3

1 answer

The formula for the volume of a square pyramid is (1/3) x (base area) x height.

First, let's find the height of the pyramid using the Pythagorean theorem:

height^2 = slant height^2 - (1/2 x base edge)^2
height^2 = 37^2 - (24/2)^2
height^2 = 1369 - 288
height^2 = 1081
height = 32.91 cm

Now, let's find the area of the base:

base area = (side length)^2
base area = 24^2
base area = 576 cm^2

Finally, we can calculate the volume:

volume = (1/3) x (base area) x height
volume = (1/3) x 576 x 32.91
volume = 10080 cm^3

Therefore, the answer is c) 10080 cm^3.