A solid cylinder of diameter 12 cm and height 15 cm is melted and recast into 12 toys in the shape of a right circular cone mounted on a hemisphere.Find the radius of the hemisphere and total height of the toy.if the height of the cone is 3 time the radius .

Explanation

To solve the problem step by step, we will follow the process of calculating the volume of the cylinder, determining the volume of the toys (which are made up of a cone and a hemisphere), and then finding the radius of the hemisphere and the total height of the toy.

### Step 1: Calculate the Volume of the Cylinder
The formula for the volume of a cylinder is given by:
\[ V = \pi r^2 h \]
Where:
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