10 conical Joker.s caps with radius 14 cm and height 48 cm are to be made using paper sheet. Find the area (in `cm^(2)`) of paper sheet required.

Answer

To find the area of paper sheet required for making 10 conical Joker's caps, we need to calculate the curved surface area of one conical cap and then multiply it by 10.

### Step 1: Identify the given values
- Radius (r) = 14 cm
- Height (h) = 48 cm

### Step 2: Calculate the slant height (l) of the cone
The slant height (l) can be calculated using the Pythagorean theorem:
\[ l = \sqrt{h^2 + r^2} \]
Substituting the values:
\[ l = \sqrt{48^2 + 14^2} \]
\[ l = \sqrt{2304 + 196} \]
\[ l = \sqrt{2500} \]
\[ l = 50 \, \text{cm} \]

### Step 3: Calculate the curved surface area (CSA) of one conical cap
The formula for the curved surface area of a cone is:
\[ \text{CSA} = \pi r l \]
Using \( \pi \approx \frac{22}{7} \):
\[ \text{CSA} = \frac{22}{7} \times 14 \times 50 \]
\[ \text{CSA} = \frac{22 \times 14 \times 50}{7} \]
\[ \text{CSA} = \frac{15400}{7} \]
\[ \text{CSA} = 2200 \, \text{cm}^2 \]

### Step 4: Calculate the total area for 10 caps
To find the total area of paper sheet required for 10 caps:
\[ \text{Total Area} = 10 \times \text{CSA} \]
\[ \text{Total Area} = 10 \times 2200 \]
\[ \text{Total Area} = 22000 \, \text{cm}^2 \]

### Final Answer
The area of paper sheet required for making 10 conical Joker's caps is **22000 cm²**.