The radius of the base of a conical tent is 16 metre. If `427(3)/(7)` sq. metre canvas is required to construct the tent, then the slant height of the tent is :
(Take `pi = (22)/(7)`)

Options

A. 17 metre
B. 15 metre
C. 19 metre
D. 8.5 metre

Answer

To find the slant height of the conical tent, we can use the formula for the curved surface area (CSA) of a cone, which is given by:

\[ \text{CSA} = \pi r l \]

where:
- \( r \) is the radius of the base,
- \( l \) is the slant height,
- \( \pi \) is a constant (approximately 3.14, but in this case, we will use \( \frac{22}{7} \)).

### Step 1: Identify the given values
- Radius \( r = 16 \) meters
- Canvas area (CSA) = \( \frac{4273}{7} \) square meters
- \( \pi = \frac{22}{7} \)

### Step 2: Set up the equation using the CSA formula
Substituting the known values into the CSA formula:

\[ \frac{4273}{7} = \frac{22}{7} \times 16 \times l \]

### Step 3: Simplify the equation
Multiply both sides by 7 to eliminate the denominator:

\[ 4273 = 22 \times 16 \times l \]

### Step 4: Calculate \( 22 \times 16 \)
Calculate \( 22 \times 16 \):

\[ 22 \times 16 = 352 \]

### Step 5: Substitute back into the equation
Now substitute back into the equation:

\[ 4273 = 352l \]

### Step 6: Solve for \( l \)
Divide both sides by 352 to isolate \( l \):

\[ l = \frac{4273}{352} \]

### Step 7: Simplify the fraction
To simplify \( \frac{4273}{352} \):

1. First, perform the division:
- \( 4273 \div 352 \approx 12.14 \) (using a calculator).

2. To find the exact value, we can also express \( 4273 \) as \( 4273 = 12 \times 352 + 49 \) (since \( 12 \times 352 = 4224 \) and \( 4273 - 4224 = 49 \)).
- Thus, \( l = 12 + \frac{49}{352} \).

### Step 8: Convert to a decimal
Calculating \( \frac{49}{352} \) gives approximately \( 0.14 \), so:

\[ l \approx 12.14 \text{ meters} \]

### Step 9: Final answer
Thus, the slant height \( l \) of the conical tent is approximately \( 12.14 \) meters.

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