A conical tent is 48 m high and the diameter of its base is 28 m . The cost of the convas required to make the tent at the rate of Rs 50 per square metre is ________.

Options

A. Rs `110,000`
B. Rs `105,600`
C. Rs `11,000`
D. Rs `127,400`

Answer

To solve the problem of finding the cost of the canvas required to make a conical tent, we will follow these steps:

### Step 1: Identify the dimensions of the cone
- The height (h) of the conical tent is given as 48 m.
- The diameter of the base is given as 28 m, so the radius (r) can be calculated as:
\[ r = \frac{\text{Diameter}}{2} = \frac{28}{2} = 14 \text{ m} \]

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

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

### Step 4: Calculate the cost of the canvas
- The cost of the canvas is given as Rs. 50 per square meter. Therefore, the total cost can be calculated as:
\[ \text{Total Cost} = \text{CSA} \times \text{Cost per m}^2 \]
- Substituting the values:
\[ \text{Total Cost} = 2200 \times 50 = 110000 \text{ Rs.} \]

### Final Answer
The cost of the canvas required to make the tent is **Rs. 110000**.

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