A conical tent is 9 m high and the radius of its base is 12 m. What is the area of canvas required to cover it?

Options

A. `180pi` square meters
B. `80pi` square meters
C. `120pi` square meters
D. `100pi` square meters

Answer

To find the area of canvas required to cover a conical tent, we need to calculate the lateral surface area of the cone. The formula for the lateral surface area (A) of a cone is given by:

\[ A = \pi r l \]

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

### Step 1: Identify the given values
From the problem, we know:
- Height (h) of the cone = 9 m
- Radius (r) of the base = 12 m

### Step 2: Calculate the slant height (l)
To find the slant height, we can use the Pythagorean theorem. The slant height (l) can be calculated using the formula:

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

Substituting the known values:

\[ l = \sqrt{9^2 + 12^2} \]
\[ l = \sqrt{81 + 144} \]
\[ l = \sqrt{225} \]
\[ l = 15 \, \text{m} \]

### Step 3: Calculate the lateral surface area (A)
Now that we have the slant height, we can substitute the values into the lateral surface area formula:

\[ A = \pi r l \]
\[ A = \pi \times 12 \times 15 \]
\[ A = 180\pi \, \text{m}^2 \]

### Conclusion
The area of canvas required to cover the conical tent is \( 180\pi \, \text{m}^2 \).

---