What length of tarpaulin `3 m` wide will be required to make conical tent of height `8 m` and base radius `6 m`? Assume that the extra length of material that will be required for stitching margins and wastage in cutting is approximately `20 cm`.

Options

A. `63`
B. `64`
C. `65`
D. `66`

Explanation

To find the length of tarpaulin required to make a conical tent, we will follow these steps:

### Step 1: Calculate the Slant Height of the Cone
The slant height (l) of a cone can be calculated using the Pythagorean theorem:
\[ l = \sqrt{h^2 + r^2} \]
where \( h \) is the height and \( r \) is the radius.

Given:
- Height \( h = 8 \, \text{m} \)
- Radius \( r = 6 \, \text{m} \)

Calculating:
\[ l = \sqrt{8^2 + 6^2} = \sqrt{64 + 36} = \sqrt{100} = 10 \, \text{m} \]

### Step 2: Calculate the Curved Surface Area of the Cone
The curved surface area (CSA) of a cone is given by the formula:
\[ \text{CSA} = \pi r l \]

Using \( \pi \approx \frac{22}{7} \):
\[ \text{CSA} = \frac{22}{7} \times 6 \times 10 \]

Calculating:
\[ \text{CSA} = \frac{22 \times 60}{7} = \frac{1320}{7} \approx 188.57 \, \text{m}^2 \]

### Step 3: Relate the Area of the Tarpaulin to the Curved Surface Area
The area of the tarpaulin is equal to the curved surface area of the cone:
\[ \text{Area of Tarpaulin} = \text{CSA} \]

### Step 4: Calculate the Length of the Tarpaulin
The area of the tarpaulin can also be expressed as:
\[ \text{Area} = \text{Length} \times \text{Breadth} \]

Given that the breadth of the tarpaulin is \( 3 \, \text{m} \):
\[ \text{Length} \times 3 = 188.57 \]

Solving for Length:
\[ \text{Length} = \frac{188.57}{3} \approx 62.86 \, \text{m} \]

### Step 5: Account for Extra Length for Stitching and Wastage
The problem states that an extra length of \( 20 \, \text{cm} \) (or \( 0.2 \, \text{m} \)) is needed for stitching and wastage.

Total Length required:
\[ \text{Total Length} = 62.86 + 0.2 = 63.06 \, \text{m} \]

### Final Answer
The length of tarpaulin required is approximately:
\[ \text{Total Length} \approx 63.06 \, \text{m} \]