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 with a height of 8 m and a base radius of 6 m, 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:
\[ l = \sqrt{r^2 + h^2} \]
where \( r \) is the radius and \( h \) is the height.

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

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

### Step 2: Calculate the Curved Surface Area of the Cone
The curved surface area \( A \) of a cone is given by the formula:
\[ A = \pi r l \]
Using \( \pi \approx 3.14 \):
\[ A = 3.14 \times 6 \times 10 = 188.4 \, \text{m}^2 \]

### Step 3: Relate the Area of the Tarpaulin to its Dimensions
The area of the tarpaulin cloth can also be expressed as:
\[ \text{Area} = \text{Length} \times \text{Width} \]
Let \( x \) be the length of the tarpaulin and the width is given as 3 m:
\[ x \times 3 = 188.4 \]

### Step 4: Solve for the Length of the Tarpaulin
Rearranging the equation to find \( x \):
\[ x = \frac{188.4}{3} = 62.8 \, \text{m} \]

### Step 5: Account for Extra Length for Stitching and Wastage
The problem states that an extra length of 20 cm (which is 0.2 m) is needed for stitching margins and wastage. Therefore, we add this to the length calculated:
\[ \text{Total Length} = 62.8 + 0.2 = 63 \, \text{m} \]

### Final Answer
The length of tarpaulin required to make the conical tent is **63 meters**.

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