What is the volume of a square pyramid with base edge of 13 mm and a slant height of 12.8 mm?

Answer 1

To find the volume of a square pyramid, you can use the formula:

Volume = (1/3) * base area * height

First, find the base area of the square pyramid:

Base area = (13 mm)^2 = 169 mm^2

Next, find the height of the pyramid using the slant height and the base edge:

Height = sqrt((slant height)^2 - ((base edge)/2)^2)
Height = sqrt((12.8 mm)^2 - (6.5 mm)^2)
Height = sqrt(163.84 mm^2 - 42.25 mm^2)
Height = sqrt(121.59 mm^2)
Height = 11.02 mm

Now, plug the values into the volume formula:

Volume = (1/3) * (169 mm^2) * (11.02 mm)
Volume = (1/3) * 1867.38 mm^3
Volume = 622.46 mm^3

Therefore, the volume of the square pyramid is 622.46 mm^3.