The base radius and height of a conical tent are 8 m and 15 m respectively. Find the area of the cloth used in this tent.

Answer

To find the area of the cloth used in a conical tent, we need to calculate the curved surface area (CSA) of the cone. The formula for the curved surface area of a cone is given by:

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

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

### Step 1: Identify the given values
From the problem, we have:
- Base radius \( r = 8 \) m
- Height \( h = 15 \) m

### Step 2: Calculate the slant height \( l \)
To find the slant height \( l \), we can use the Pythagorean theorem, which states:

\[ l = \sqrt{r^2 + h^2} \]

Substituting the values of \( r \) and \( h \):

\[ l = \sqrt{8^2 + 15^2} \]

Calculating \( r^2 \) and \( h^2 \):

\[ l = \sqrt{64 + 225} \]
\[ l = \sqrt{289} \]
\[ l = 17 \text{ m} \]

### Step 3: Calculate the curved surface area (CSA)
Now that we have \( l \), we can substitute \( r \) and \( l \) into the CSA formula:

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

Using \( \pi \approx \frac{22}{7} \):

\[ \text{CSA} = \frac{22}{7} \times 8 \times 17 \]

Calculating the multiplication:

\[ \text{CSA} = \frac{22 \times 8 \times 17}{7} \]
\[ = \frac{2976}{7} \]
\[ \approx 425.14 \text{ m}^2 \]

### Step 4: Final answer
Thus, the area of the cloth used in the tent is approximately:

\[ \text{CSA} \approx 425.14 \text{ m}^2 \]