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
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
To find the volume of a square pyramid, you can use the formula:
Volume = (1/3) * (Base Area) * Height
In this case, the base edges of the square pyramid are given as 24 cm, and the slant height is given as 37 cm. The base area can be computed by finding the area of the square base. Since all edges of a square are equal, each edge of the square base is also 24 cm.
Base Area = (Edge length)^2
Base Area = 24 cm * 24 cm
Base Area = 576 cm^2
Using the formula for the volume:
Volume = (1/3) * (576 cm^2) * 37 cm
Calculating the value:
Volume = (1/3) * 576 cm^2 * 37 cm
Volume = 192 cm^2 * 37 cm
Volume = 7104 cm^3
Therefore, the volume of the square pyramid is 7104 cm^3.