A conical tent with radius 5 m and slant height 14 m is to be made. How many metres of 2 m wide tarpaulin will be required ?

Answer

To solve the problem of how many meters of 2 m wide tarpaulin will be required to cover a conical tent with a radius of 5 m and a slant height of 14 m, we will follow these steps:

### Step 1: Calculate the Curved Surface Area of the Cone
The formula for the curved surface area (CSA) of a cone is given by:
\[ \text{CSA} = \pi r l \]
where \( r \) is the radius and \( l \) is the slant height.

Given:
- Radius \( r = 5 \) m
- Slant height \( l = 14 \) m
- We will use \( \pi \approx \frac{22}{7} \)

Substituting the values into the formula:
\[ \text{CSA} = \frac{22}{7} \times 5 \times 14 \]

### Step 2: Perform the Multiplication
Calculating the multiplication:
\[ \text{CSA} = \frac{22}{7} \times 5 \times 14 = \frac{22 \times 5 \times 14}{7} \]
First, calculate \( 5 \times 14 = 70 \):
\[ \text{CSA} = \frac{22 \times 70}{7} \]
Now, simplify \( \frac{70}{7} = 10 \):
\[ \text{CSA} = 22 \times 10 = 220 \text{ m}^2 \]

### Step 3: Calculate the Length of Tarpaulin Required
The area of the tarpaulin required can be calculated using the formula for the area of a rectangle:
\[ \text{Area} = \text{Length} \times \text{Breadth} \]
Here, the breadth of the tarpaulin is given as 2 m. We need to find the length of the tarpaulin required to cover the curved surface area of the cone:
\[ \text{Length} = \frac{\text{CSA}}{\text{Breadth}} = \frac{220 \text{ m}^2}{2 \text{ m}} = 110 \text{ m} \]

### Final Answer
Thus, the length of the tarpaulin required is:
\[ \text{Length of tarpaulin required} = 110 \text{ m} \]

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