Find what length of canvas, 1.5 m in width, is required to make a conical tent 48 m diameter and 7 m in height ? Given that 10% of the canvas is used in folds and stitchings. Also, find the cost of the canvas at the rate of Rs.24 per metre.

Answer

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

### Step 1: Identify the given values
- Diameter of the conical tent (D) = 48 m
- Height of the conical tent (h) = 7 m
- Width of the canvas (b) = 1.5 m
- Additional canvas for folds and stitching = 10%

### Step 2: Calculate the radius of the cone
The radius (r) is half of the diameter:
\[ r = \frac{D}{2} = \frac{48}{2} = 24 \text{ m} \]

### Step 3: Calculate the slant height (l) of the cone
Using the Pythagorean theorem:
\[ l = \sqrt{r^2 + h^2} = \sqrt{24^2 + 7^2} = \sqrt{576 + 49} = \sqrt{625} = 25 \text{ m} \]

### Step 4: Calculate the curved surface area (CSA) of the cone
The formula for the curved surface area of a cone is:
\[ \text{CSA} = \pi r l \]
Substituting the values:
\[ \text{CSA} = \frac{22}{7} \times 24 \times 25 \]
Calculating this:
\[ \text{CSA} = \frac{22 \times 24 \times 25}{7} = \frac{13200}{7} \text{ m}^2 \]

### Step 5: Calculate the total area of canvas required
Since 10% of the canvas is used for folds and stitching, the total area needed is:
\[ \text{Total Area} = \text{CSA} \times \frac{110}{100} = \frac{13200}{7} \times 1.1 = \frac{14520}{7} \text{ m}^2 \]

### Step 6: Relate the area of the canvas to its length
The area of the rectangular canvas is given by:
\[ \text{Area} = \text{Length} \times \text{Width} = L \times 1.5 \]
Setting this equal to the total area needed:
\[ L \times 1.5 = \frac{14520}{7} \]
Solving for L:
\[ L = \frac{14520}{7 \times 1.5} = \frac{14520}{10.5} = \frac{14520 \div 10.5}{1} = \frac{1380}{1} = 1380 \text{ m} \]

### Step 7: Calculate the cost of the canvas
The cost of the canvas per meter is Rs. 24. Therefore, the total cost is:
\[ \text{Total Cost} = L \times \text{Cost per meter} = 1380 \times 24 \]
Calculating this:
\[ \text{Total Cost} = 33120 \text{ Rs} \]

### Final Answers
- Length of canvas required = 1380 m
- Cost of the canvas = Rs. 33120

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