What is the volume of a square pyramid with base edges of 24 cm and a slant height of 37 cm?
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.
To find the volume of a square pyramid, you can use the formula:
Volume = (1/3) * base area * height
In this case, the base of the pyramid is a square with edge length of 24 cm. Therefore, the base area can be calculated as:
Base area = length of edge * length of edge = 24 cm * 24 cm = 576 cm²
Now we need to determine the height of the pyramid. The slant height is given as 37 cm, which is the distance from the apex of the pyramid to the midpoint of one of the edges of the base. The height of the pyramid can be obtained using the Pythagorean theorem:
Height² = slant height² - (length of half an edge)²
Height² = 37 cm² - (12 cm)²
Height² = 37 cm² - 144 cm²
Height² = 1369 cm² - 144 cm²
Height² = 1225 cm²
Taking the square root of both sides, we find:
Height = √(1225 cm²)
Height ≈ 35 cm
Now we can substitute these values into the volume formula:
Volume = (1/3) * base area * height
Volume = (1/3) * 576 cm² * 35 cm
Volume = 20160 cm³
Therefore, the volume of the square pyramid is approximately 20160 cm³.