A circus tent is cylindrical to a height of 8 m surmounted by a conical part. If total height of the tent is 13 m and the diameter of its base is 24 m, calculate :
area of canvas, required to make this tent allowing 10% of the canvas used for folds and stitching

Answer

To solve the problem of calculating the area of canvas required to make a circus tent, we will follow these steps:

### Step 1: Understand the dimensions of the tent
- The tent consists of a cylindrical part and a conical part.
- The height of the cylindrical part (h_cylinder) = 8 m.
- The total height of the tent (h_total) = 13 m.
- Therefore, the height of the conical part (h_cone) = h_total - h_cylinder = 13 m - 8 m = 5 m.
- The diameter of the base of the tent = 24 m, so the radius (r) = diameter / 2 = 24 m / 2 = 12 m.

### Step 2: Calculate the slant height of the cone
To find the slant height (l) of the conical part, we can use the Pythagorean theorem:
- We have a right triangle where:
- One leg is the height of the cone (h_cone) = 5 m.
- The other leg is the radius of the base (r) = 12 m.

Using the Pythagorean theorem:
\[ l = \sqrt{(h_{cone})^2 + (r)^2} = \sqrt{(5)^2 + (12)^2} = \sqrt{25 + 144} = \sqrt{169} = 13 \, \text{m} \]

### Step 3: Calculate the surface area of the tent
The total surface area of the tent consists of the curved surface area of the cylindrical part and the curved surface area of the conical part.

- **Curved Surface Area of the Cylinder (CSA_cylinder)**:
\[ \text{CSA}_{cylinder} = 2 \pi r h_{cylinder} = 2 \times \frac{22}{7} \times 12 \times 8 \]

Calculating:
\[ \text{CSA}_{cylinder} = 2 \times \frac{22}{7} \times 12 \times 8 = \frac{4224}{7} \, \text{m}^2 \]

- **Curved Surface Area of the Cone (CSA_cone)**:
\[ \text{CSA}_{cone} = \pi r l = \frac{22}{7} \times 12 \times 13 \]

Calculating:
\[ \text{CSA}_{cone} = \frac{22}{7} \times 12 \times 13 = \frac{2856}{7} \, \text{m}^2 \]

- **Total Surface Area of the Tent (TSA)**:
\[ \text{TSA} = \text{CSA}_{cylinder} + \text{CSA}_{cone} = \frac{4224}{7} + \frac{2856}{7} = \frac{7080}{7} \, \text{m}^2 \]

### Step 4: Calculate the total area of canvas required
The total area of canvas required includes an additional 10% for folds and stitching.

Let \( A \) be the area of canvas required. Then:
\[ A + 0.1A = \text{TSA} \]
\[ 1.1A = \text{TSA} \]
\[ A = \frac{\text{TSA}}{1.1} \]

Calculating:
\[ A = \frac{\frac{7080}{7}}{1.1} = \frac{7080}{7 \times 1.1} = \frac{7080}{7.7} \approx 920.78 \, \text{m}^2 \]

### Final Answer
The area of canvas required to make the tent, allowing for 10% for folds and stitching, is approximately **920.78 m²**.