A joker's cap is in the form of a right circular cone of base radius 7 cm and height 24 cm. Find the area of the sheet required to make 10 such caps.

Answer

To find the area of the sheet required to make 10 joker caps in the shape of a right circular cone, we need to follow these steps:

### Step 1: Calculate the Slant Height (L) of the Cone
The formula for the slant height \( L \) of a cone is given by:
\[ L = \sqrt{h^2 + r^2} \]
where \( h \) is the height and \( r \) is the radius of the base.

Given:
- Height \( h = 24 \) cm
- Radius \( r = 7 \) cm

Now, substituting the values:
\[ L = \sqrt{24^2 + 7^2} = \sqrt{576 + 49} = \sqrt{625} = 25 \text{ cm} \]

### Step 2: Calculate the Curved Surface Area (CSA) of One Cone
The formula for the curved surface area \( A \) of a cone is:
\[ A = \pi r L \]
Using \( \pi \approx \frac{22}{7} \):
\[ A = \frac{22}{7} \times 7 \times 25 \]
Simplifying this:
\[ A = 22 \times 25 = 550 \text{ cm}^2 \]

### Step 3: Calculate the Total Area for 10 Caps
To find the area of the sheet required for 10 caps, we multiply the curved surface area of one cap by 10:
\[ \text{Total Area} = 10 \times A = 10 \times 550 = 5500 \text{ cm}^2 \]

### Final Answer
The area of the sheet required to make 10 joker caps is:
\[ \text{Total Area} = 5500 \text{ cm}^2 \]

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