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 ?

Question

Accepted Answer

To determine 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 of a cone is given by:

$$ \text{Lateral Surface Area} = \pi r l $$

where $ r $ is the radius of the base of the cone, and $ l $ is the slant height of the cone.

Given:
- Height ($ h $) of the cone = 9 m
- Radius ($ r $) of the base = 12 m

First, we need to find the slant height ($ l $) of the cone using the Pythagorean theorem:

$$ l = \sqrt{r^2 + h^2} $$

Substituting the given values:

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

Now, we can calculate the lateral surface area:

$$ \text{Lateral Surface Area} = \pi \times 12 \times 15 $$
$$ \text{Lateral Surface Area} = 180\pi \, \text{square meters} $$

Thus, the area of canvas required to cover the conical tent is $ 180\pi $ square meters, which corresponds to Option 1.

**Explanation for Incorrect Options:**

- **Option 2: $80\pi$ square meters**  
  This option is incorrect because it significantly underestimates the lateral surface area. The calculation using the correct formula and values clearly shows that the area is $ 180\pi $, not $ 80\pi $.

- **Option 3: $120\pi$ square meters**  
  This option is also incorrect as it does not match the calculated lateral surface area. The correct calculation yields $ 180\pi $, which is greater than $ 120\pi $.

- **Option 4: $100\pi$ square meters**  
  This option is incorrect because it is not consistent with the calculated lateral surface area. The correct value is $ 180\pi $, which is much larger than $ 100\pi $.

In conclusion, the correct area of canvas required to cover the conical tent is $ 180\pi $ square meters, making Option 1 the correct choice.