We can use the formula for the volume of a pyramid, which is:
V = (1/3) x base area x height
In a square pyramid, the base area is the area of the square base, which is:
base area = (side length)^2 = 24^2 = 576 cm^2
The height of the pyramid is the perpendicular distance from the apex (top) of the pyramid to the base. In this case, we don't know the height directly, but we can use the slant height and the Pythagorean theorem to find it:
height^2 + (side length/2)^2 = slant height^2
height^2 + 12^2 = 37^2
height^2 = 37^2 - 12^2
height^2 = 1297
height = sqrt(1297) ≈ 36.02 cm
Now we can plug in the values for the base area and height to find the volume:
V = (1/3) x 576 x 36.02
V = 6,469.12 cm^3
Therefore, the volume of the pyramid is approximately 6,469.12 cubic centimeters.
What is the volume of a square pyramid with base edges of 24 cm and a slant height of 37 cm?
1 answer