The diameter and the slant height of a conical tent are 16 m and 5 .6 m. respectively. What length of cloth having width 4 m is needed to make the tent?

Options

A. 35.2 m
B. 32.5 m
C. 32 m
D. 35 m

Answer

To determine the length of cloth needed to make the conical tent, we first need to calculate the surface area of the conical tent, which is given by the formula for the lateral surface area of a cone. The formula is:

\[ \text{Lateral Surface Area} = \pi r l \]

where:
- \( r \) is the radius of the base of the cone,
- \( l \) is the slant height of the cone.

### Step 1: Calculate the radius of the cone
Given that the diameter of the conical tent is 16 m, we can find the radius \( r \) as follows:

\[ r = \frac{\text{Diameter}}{2} = \frac{16 \, \text{m}}{2} = 8 \, \text{m} \]

### Step 2: Identify the slant height
The slant height \( l \) is given as 5.6 m.

### Step 3: Calculate the lateral surface area
Now we can substitute the values of \( r \) and \( l \) into the formula for lateral surface area:

\[ \text{Lateral Surface Area} = \pi r l = \pi \times 8 \, \text{m} \times 5.6 \, \text{m} \]

Using \( \pi \approx 3.14 \):

\[ \text{Lateral Surface Area} \approx 3.14 \times 8 \times 5.6 \]

Calculating this:

\[ \text{Lateral Surface Area} \approx 3.14 \times 44.8 \approx 140.608 \, \text{m}^2 \]

### Step 4: Calculate the length of cloth needed
The width of the cloth is given as 4 m. To find the length of cloth needed, we divide the lateral surface area by the width of the cloth:

\[ \text{Length of cloth} = \frac{\text{Lateral Surface Area}}{\text{Width}} = \frac{140.608 \, \text{m}^2}{4 \, \text{m}} \]

Calculating this:

\[ \text{Length of cloth} \approx 35.152 \, \text{m} \]

### Step 5: Round to the nearest option
Rounding 35.152 m gives us approximately 35.2 m.

### Final Answer
The length of cloth needed to make the tent is approximately **35.2 meters**.

---