Acone 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.

The volume of the cone is  equal to

Step-by-step explanation:

we know that

The volume of a cone is equal to

where

r is the radius of the base

h is the height of the cone

In this problem the length of the square base of the pyramid is equal to the diameter of the base of the cone

so

Step 1

Find the height of the cone

Applying the Pythagoras Theorem

where

l is the slant height

in this problem we have

Solve for h

substitute the values

Step 2

Find the volume of the cone

we have

substitute the values

d. it is a convex pentagon because it has five sides and none of the sides would extend into the inside of the polygon.

step-by-step explanation:

answer: the answer is d