Question

A cone is inscribed in a regular square pyramid. If the pyramid has a base edge of 6" and a slant height of 9", find the volume of the cone.

Answer 1

area of the cone will equal 1/3 (area of the base) (height)

for the area of the base, we know that the cone has a diameter of 6" (since it is the largest possible circle inside the square base). so use the area of a circle formula to get:

(pi)r^2 where r=3 (1/2 of 6)
9(pi)

the height is a little tickier, since you know the slant height, you need to use the properties of a right triangle to get the height. The hypotenuse is 9" and the base is 3" so we use

a^2 + b^2 = c^2
3^2 + b^2= 9^2
9+b^2=81
b^2=72
b=8.49

now that you have the height and the area of the base, put it all together to get:

1/3 (9(pi))(8.49)

your answer is 25.47 in^3