How many metres of cloth 50 m wide will be required to make a conical tent, the radius of whose base is 7m and whose height is 24 m ?

Options

A. 11 m
B. 50 m
C. 550 m
D. None of these

Answer

To determine how many meters of cloth 50 m wide will be required to make a conical tent with a base radius of 7 m and a height of 24 m, we will follow these steps:

### Step 1: Calculate the Slant Height of the Cone
The slant height (L) of a cone can be calculated using the Pythagorean theorem:
\[ L = \sqrt{h^2 + r^2} \]
where \(h\) is the height of the cone and \(r\) is the radius of the base.

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

Calculating:
\[ L = \sqrt{24^2 + 7^2} = \sqrt{576 + 49} = \sqrt{625} = 25 \text{ m} \]

### Step 2: Calculate the Curved Surface Area of the Cone
The formula for the curved surface area (CSA) of a cone is given by:
\[ \text{CSA} = \pi r L \]
Substituting the values:
\[ \text{CSA} = \pi \times 7 \times 25 \]
Using \(\pi \approx \frac{22}{7}\):
\[ \text{CSA} = \frac{22}{7} \times 7 \times 25 \]
The \(7\) in the numerator and denominator cancels out:
\[ \text{CSA} = 22 \times 25 = 550 \text{ m}^2 \]

### Step 3: Calculate the Length of Cloth Required
The width of the cloth is given as 50 m. To find the length of cloth required, we use the formula:
\[ \text{Length of cloth} = \frac{\text{Curved Surface Area}}{\text{Width of cloth}} \]
Substituting the values:
\[ \text{Length of cloth} = \frac{550}{50} = 11 \text{ m} \]

### Conclusion
The total length of cloth required to make the conical tent is **11 meters**.

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