The radius of the base of a Conical tent is 12 m. The tent is 9 m high. Find the cost of canvas required to make the tent, if one square metre of canvas costs Rs 120
(Take `pi = 3.14`)

Options

A. Rs. 67,830
B. Rs. 67,800
C. Rs. 67,820
D. Rs. 67,824

Answer

To find the cost of the canvas required to make the conical tent, we need to follow these steps:

### Step 1: Identify the given values
- Radius of the base of the cone (r) = 12 m
- Height of the cone (h) = 9 m
- Cost of canvas per square meter = Rs 120
- Value of π (pi) = 3.14

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

### 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:
\[ \text{CSA} = 3.14 \times 12 \times 15 \]
\[ \text{CSA} = 3.14 \times 180 \]
\[ \text{CSA} = 565.2 \, m^2 \]

### Step 4: Calculate the cost of the canvas
To find the total cost, multiply the curved surface area by the cost per square meter:
\[ \text{Total Cost} = \text{CSA} \times \text{Cost per m}^2 \]
Substituting the values:
\[ \text{Total Cost} = 565.2 \times 120 \]
\[ \text{Total Cost} = 67824 \, \text{Rs} \]

### Final Answer
The cost of the canvas required to make the tent is Rs 67824.

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