How much cloth 2.5 m wide will be required to make a conical tent having base radius 7 m and height 24 m ?

Options

A. 120 m
B. 180 m
C. 220 m
D. 550 m

Explanation

To find out how much cloth is 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 (L)
The slant height (L) of the cone can be calculated using the Pythagorean theorem. The formula is:
\[ L = \sqrt{h^2 + r^2} \]
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:
\[ L = \sqrt{24^2 + 7^2} \]
\[ L = \sqrt{576 + 49} \]
\[ L = \sqrt{625} \]
\[ L = 25 \, \text{m} \]

### Step 2: Calculate the Curved Surface Area (CSA) of the Cone
The curved surface area (CSA) of a cone is given by the formula:
\[ \text{CSA} = \pi r L \]

Using \( \pi \approx \frac{22}{7} \):
\[ \text{CSA} = \frac{22}{7} \times 7 \times 25 \]
\[ \text{CSA} = 22 \times 25 \]
\[ \text{CSA} = 550 \, \text{m}^2 \]

### Step 3: Determine the Width of the Cloth
The width of the cloth is given as 2.5 m.

### Step 4: Calculate the Length of Cloth Required
Let the length of the cloth required be \( X \). The area of the rectangular cloth can be expressed as:
\[ \text{Area of cloth} = \text{Length} \times \text{Width} = X \times 2.5 \]

We set the area of the cloth equal to the curved surface area of the cone:
\[ X \times 2.5 = 550 \]

Now solve for \( X \):
\[ X = \frac{550}{2.5} \]
\[ X = 220 \, \text{m} \]

### Conclusion
The length of cloth required to make the conical tent is **220 meters**.

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