Volume Of A Right Circular Cone

To find out how many identical cones are formed when a solid hemisphere is melted, we need to determine the volumes of the hemisphere and a cone, and then divide the volume of the hemisphere by the volume of one cone.

Step 1: Calculate the volume of the solid hemisphere.

The formula for the volume of a hemisphere is:

Given the radius of the hemisphere ( ), the volume is:

Step 2: Calculate the volume of one cone.

The formula for the volume of a cone is:

Given the base radius of the cone ( ) and the height ( ), the volume is:

Step 3: Determine the number of cones formed.

To find the number of cones, divide the volume of the hemisphere by the volume of one cone:

Therefore, 72 identical cones are formed from the solid hemisphere.