A conical tent is 12 m high and the radius of its base is 9 m . What is the cost of canvas required to make the tent , if the cost of `1 m^(2)` canvas is Rs 14 ?

Options

A. Rs 5940
B. Rs 4752
C. Rs 5840
D. Rs 4653

Answer

To find the cost of the canvas required to make a conical tent, we need to calculate the curved surface area of the cone and then multiply it by the cost per square meter of the canvas. Here’s how we can do it step by step:

### Step 1: Identify the dimensions of the cone
- Height (h) = 12 m
- Radius (r) = 9 m

### Step 2: Calculate the slant height (l) of the cone
The slant height can be calculated using the Pythagorean theorem:
\[ l = \sqrt{h^2 + r^2} \]
\[ l = \sqrt{12^2 + 9^2} \]
\[ l = \sqrt{144 + 81} \]
\[ l = \sqrt{225} \]
\[ l = 15 \, m \]

### Step 3: Calculate the curved surface area (CSA) of the cone
The formula for the curved surface area of a cone is:
\[ \text{CSA} = \pi r l \]
Substituting the values we have:
\[ \text{CSA} = \pi \times 9 \times 15 \]
\[ \text{CSA} = 135\pi \, m^2 \]

### Step 4: Calculate the cost of the canvas
The cost of canvas per square meter is Rs 14. Therefore, the total cost can be calculated as:
\[ \text{Total Cost} = \text{CSA} \times \text{Cost per m}^2 \]
\[ \text{Total Cost} = 135\pi \times 14 \]
Using \(\pi \approx \frac{22}{7}\):
\[ \text{Total Cost} = 135 \times \frac{22}{7} \times 14 \]

### Step 5: Simplify the calculation
\[ \text{Total Cost} = 135 \times 22 \times 2 \]
\[ \text{Total Cost} = 135 \times 44 \]
\[ \text{Total Cost} = 5940 \, \text{Rs} \]

### Final Answer
The cost of the canvas required to make the tent is Rs 5940.

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