A circus tent is cylindrical to a height of 3 meters and conical above it. If the radius of the base is 52.5 m and the slant height of the cone is 52 m,then the total area of the canvas required to make it is:

Options

A. 3048 `pi`
B. `3045 pi`
C. `2730 pi`
D. `2842 pi`

Answer

To find the total area of the canvas required to make the circus tent, we need to calculate the curved surface area of both the cylindrical and conical portions of the tent.

### Step-by-Step Solution:

1. **Identify the dimensions given:**
- Height of the cylindrical part (h) = 3 meters
- Radius of the base (r) = 52.5 meters
- Slant height of the conical part (L) = 52 meters

2. **Calculate the curved surface area of the cylindrical part (S1):**
The formula for the curved surface area of a cylinder is:
\[ S1 = 2 \pi r h \]
Substituting the values:
\[ S1 = 2 \pi (52.5) (3) \]

3. **Calculate the curved surface area of the conical part (S2):**
The formula for the curved surface area of a cone is:
\[ S2 = \pi r L \]
Substituting the values:
\[ S2 = \pi (52.5) (52) \]

4. **Combine the areas to find the total area of the canvas (A):**
The total area of the canvas required is the sum of the curved surface areas of the cylinder and the cone:
\[ A = S1 + S2 \]
This can be expressed as:
\[ A = 2 \pi r h + \pi r L \]
Factoring out \(\pi r\):
\[ A = \pi r (2h + L) \]

5. **Substituting the values into the total area formula:**
\[ A = \pi (52.5) (2(3) + 52) \]
Simplifying the expression inside the parentheses:
\[ A = \pi (52.5) (6 + 52) = \pi (52.5) (58) \]

6. **Final calculation:**
\[ A = 52.5 \times 58 \times \pi \]
Calculating \(52.5 \times 58\):
\[ 52.5 \times 58 = 3045 \]
Therefore, the total area of the canvas is:
\[ A = 3045 \pi \]

### Conclusion:
The total area of the canvas required to make the circus tent is \(3045 \pi\) square meters.