The question is what is the volume of a square pyramid with base edges of 40 cm and a slant height of 25 cm.
The Volume, V, of a pyramid is V = [1/3] * area of the base * height
The base of this pyramid is a square of side 40 cm, then its area is (40cm)^2 = 1600 cm^2
The height of the pyramid is calculated using Pytagora's theorem:
(half side of the base)^2 + (height of the pyramid)^2 = (slant height)^2
=> (height of the pyramid)^2 = (slant height)^2 - (half side of the base)^2
(height of the pyramid)^2 = (25cm)^2 - (20cm)^2 = 225 cm^2
=> height of the pyramid = 15 cm
Now you can calcualte the volume of the pyramid with the formula V = [1/3](area of the base)(height)
V = [1/3](1600 cm^2)(15 cm) = 8000 cm^3
Answer: 8000 cm^3
