Shantanu'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 5 such caps.

Options

A. 5000 sq cm
B. 2750 sq cm
C. 3000 sq cm
D. 2700 sq cm

Answer

To find the area of the sheet required to make 5 caps in the shape of a right circular cone, we will follow these steps:

### Step 1: Identify the given values
- Base radius (r) of the cone = 7 cm
- Height (h) of the cone = 24 cm

### Step 2: Calculate the slant height (l) of the cone
The slant height can be calculated using the Pythagorean theorem:
\[ l = \sqrt{r^2 + h^2} \]
Substituting the values:
\[ l = \sqrt{7^2 + 24^2} = \sqrt{49 + 576} = \sqrt{625} = 25 \text{ cm} \]

### Step 3: Calculate the curved surface area (CSA) of one cap
The formula for the curved surface area of a cone is:
\[ \text{CSA} = \pi r l \]
Using \(\pi \approx \frac{22}{7}\):
\[ \text{CSA} = \frac{22}{7} \times 7 \times 25 \]
Calculating this:
\[ \text{CSA} = 22 \times 25 = 550 \text{ cm}^2 \]

### Step 4: Calculate the total area of the sheet required for 5 caps
To find the total area required for 5 caps, we multiply the area of one cap by 5:
\[ \text{Total Area} = 5 \times \text{CSA} = 5 \times 550 = 2750 \text{ cm}^2 \]

### Final Answer
The area of the sheet required to make 5 caps is **2750 cm²**.

---