A conical tent is to be built 4 m in diameter and a slant height of 5.6 m. What will be the cost of canvas required to build this tent at the rate of Rs. 3.2 per square metre ?

Options

A. Rs. 112.64
B. Rs. 110
C. Rs. 114.4
D. Rs. 108.3

Answer

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

### Step 1: Find the radius of the cone
Given the diameter of the tent is 4 meters, we can find the radius (r) using the formula:
\[ r = \frac{\text{diameter}}{2} = \frac{4 \text{ m}}{2} = 2 \text{ m} \]

**Hint:** Remember that the radius is half of the diameter.

### Step 2: Identify the slant height of the cone
The slant height (l) of the cone is given as 5.6 meters.

**Hint:** The slant height is a direct value provided in the problem.

### Step 3: Calculate the curved surface area (CSA) of the cone
The formula for the curved surface area (CSA) of a cone is:
\[ \text{CSA} = \pi r l \]
Substituting the values of \( r \) and \( l \):
\[ \text{CSA} = \pi \times 2 \text{ m} \times 5.6 \text{ m} \]
Using \( \pi \approx 3.14 \):
\[ \text{CSA} \approx 3.14 \times 2 \times 5.6 = 35.392 \text{ m}^2 \]

**Hint:** Make sure to use the correct value of \( \pi \) for your calculations.

### Step 4: Calculate the cost of the canvas
The cost of the canvas is calculated by multiplying the area by the cost per square meter. The cost is given as Rs. 3.2 per square meter.
\[ \text{Cost} = \text{CSA} \times \text{rate per square meter} \]
Substituting the values:
\[ \text{Cost} = 35.392 \text{ m}^2 \times 3.2 \text{ Rs/m}^2 = 113.2544 \text{ Rs} \]

**Hint:** Ensure to multiply the area by the cost rate correctly.

### Step 5: Round the final cost
The final cost can be rounded to two decimal places:
\[ \text{Total Cost} \approx 113.25 \text{ Rs} \]

**Hint:** Rounding is important for financial figures to maintain clarity.

### Final Answer
The cost of the canvas required to build the tent is approximately Rs. 113.25.