A circus tent is cylindrical to a height of 4 m and conical above it. If its diameter is 105 m and its slant height is 80 m, calculate the total area of canvas required. Also, find the total cost of canvas used at Rs 15 if the width is 1.5 m.

Answer

To solve the problem of calculating the total area of canvas required for the circus tent and its total cost, we can follow these steps:

### Step 1: Identify the given values
- Height of the cylindrical part (h) = 4 m
- Diameter of the tent = 105 m
- Slant height of the conical part (l) = 80 m

### Step 2: Calculate the radius of the tent
The radius (r) is half of the diameter:
\[ r = \frac{Diameter}{2} = \frac{105}{2} = 52.5 \, m \]

### Step 3: Calculate the curved surface area of the cylindrical part
The formula for the curved surface area (CSA) of a cylinder is:
\[ CSA_{cylinder} = 2 \pi r h \]
Substituting the values:
\[ CSA_{cylinder} = 2 \times \frac{22}{7} \times 52.5 \times 4 \]
Calculating this:
\[ CSA_{cylinder} = 2 \times \frac{22}{7} \times 52.5 \times 4 = \frac{22 \times 52.5 \times 8}{7} \]
\[ = \frac{9240}{7} = 1320 \, m^2 \]

### Step 4: Calculate the curved surface area of the conical part
The formula for the curved surface area of a cone is:
\[ CSA_{cone} = \pi r l \]
Substituting the values:
\[ CSA_{cone} = \frac{22}{7} \times 52.5 \times 80 \]
Calculating this:
\[ CSA_{cone} = \frac{22 \times 52.5 \times 80}{7} \]
\[ = \frac{88080}{7} = 12568.57 \, m^2 \]

### Step 5: Calculate the total area of canvas required
The total area of canvas required is the sum of the curved surface areas of the cylinder and the cone:
\[ Total \, Area = CSA_{cylinder} + CSA_{cone} \]
\[ Total \, Area = 1320 + 12568.57 = 13888.57 \, m^2 \]

### Step 6: Calculate the total cost of the canvas
The cost of canvas is given as Rs 15 for 1.5 m². First, we find the cost per m²:
\[ Cost \, per \, m² = \frac{15}{1.5} = 10 \, Rs/m² \]
Now, we can calculate the total cost:
\[ Total \, Cost = Total \, Area \times Cost \, per \, m² \]
\[ Total \, Cost = 13888.57 \times 10 = 138885.7 \, Rs \]

### Final Answers
- Total area of canvas required: \( 13888.57 \, m^2 \)
- Total cost of canvas: \( 138885.7 \, Rs \)