A solid metallic cylinder diameter 12 cm and height 15 cm is melted and recast into toys each in the shape of a cone of radius 3 cm and height 9 cm. Find the number of toys so formed.

Answer

To solve the problem, we need to find the volume of the solid metallic cylinder and the volume of one toy cone, and then determine how many cones can be formed from the volume of the cylinder.

### Step 1: Calculate the volume of the cylinder
The formula for the volume \( V \) of a cylinder is given by:
\[ V = \pi r^2 h \]
where \( r \) is the radius and \( h \) is the height.

1. **Find the radius of the cylinder**:
The diameter of the cylinder is 12 cm, so the radius \( r \) is:
\[ r = \frac{12}{2} = 6 \text{ cm} \]

2. **Height of the cylinder**:
The height \( h \) is given as 15 cm.

3. **Calculate the volume**:
\[ V_{cylinder} = \pi (6)^2 (15) = \pi (36)(15) = 540\pi \text{ cm}^3 \]

### Step 2: Calculate the volume of one cone
The formula for the volume \( V \) of a cone is given by:
\[ V = \frac{1}{3} \pi r^2 h \]
where \( r \) is the radius and \( h \) is the height.

1. **Radius of the cone**:
The radius is given as 3 cm.

2. **Height of the cone**:
The height is given as 9 cm.

3. **Calculate the volume**:
\[ V_{cone} = \frac{1}{3} \pi (3)^2 (9) = \frac{1}{3} \pi (9)(9) = \frac{81}{3} \pi = 27\pi \text{ cm}^3 \]

### Step 3: Find the number of cones that can be formed
To find the number of cones that can be formed from the volume of the cylinder, we divide the volume of the cylinder by the volume of one cone:
\[ \text{Number of cones} = \frac{V_{cylinder}}{V_{cone}} = \frac{540\pi}{27\pi} \]
The \( \pi \) cancels out:
\[ \text{Number of cones} = \frac{540}{27} = 20 \]

### Final Answer
The number of toys (cones) that can be formed is **20**.

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