What is the volume of a square pyramid with base edges of 24 cm and a slant height of 33 cm?(1 point) Responses 6326.5 cm336326.5 cm3 2261.5 cm332261.5 cm3 6336.0 cm336336.0 cm3 5902.2 cm3
To find the volume of a square pyramid, use the formula V = (1/3) * B * h, where B is the area of the base and h is the height of the pyramid.
First, calculate the area of the base:
A = (24 cm)^2 = 576 cm^2
Now, using the Pythagorean theorem, we can find the height of the pyramid:
h = √(33 cm)^2 - (12 cm)^2
h = √(1089 cm^2 - 144 cm^2)
h = √945 cm^2
h = 30.74 cm
Now plug in the values into the formula:
V = (1/3) * 576 cm^2 * 30.74 cm
V = 5902.2 cm^3
Therefore, the volume of the square pyramid is 5902.2 cm^3.