A bus stop is barricated from the remaining part of the road by using 50 hollow cones made of recycled cardboard. Each one has a base diameter of 40 cm and height 1m. If the outer side of each of the cones is to be painted and the cost of painting is Rs 25 per `m^(2)`, what will be the cost of painting all these cone ? (Use `pi = 3.14 and sqrt(1.04) = 1.02`)

Explanation

To solve the problem step by step, we will follow these calculations:

### Step 1: Determine the radius and height of the cone
- Given the base diameter of the cone is 40 cm, we can find the radius (R) by dividing the diameter by 2.

\[ R = \frac{40 \text{ cm}}{2} = 20 \text{ cm} = 0.2 \text{ m} \quad (\text{since } 1 \text{ m} = 100 \text{ cm}) \]

- The height (h) of the cone is given as 1 m.

### Step 2: Calculate the slant height (L) of the cone
- The slant height can be calculated using the Pythagorean theorem:

\[ L = \sqrt{R^2 + h^2} \]

Substituting the values:

\[ L = \sqrt{(0.2)^2 + (1)^2} = \sqrt{0.04 + 1} = \sqrt{1.04} \approx 1.02 \text{ m} \]

### Step 3: Calculate the curved surface area (CSA) of one cone
- The formula for the curved surface area of a cone is:

\[ \text{CSA} = \pi R L \]

Substituting the values of \( \pi \), \( R \), and \( L \):

\[ \text{CSA} = 3.14 \times 0.2 \times 1.02 \]

Performing the multiplication:

\[ \text{CSA} \approx 3.14 \times 0.2 \times 1.02 = 0.64 \text{ m}^2 \]

### Step 4: Calculate the total curved surface area for 50 cones
- Since there are 50 cones, the total curved surface area (TCSA) is:

\[ \text{TCSA} = 50 \times \text{CSA} = 50 \times 0.64 = 32 \text{ m}^2 \]

### Step 5: Calculate the cost of painting
- The cost of painting is given as Rs 25 per m². Therefore, the total cost (C) can be calculated as:

\[ C = \text{TCSA} \times \text{cost per m}^2 = 32 \times 25 \]

Performing the multiplication:

\[ C = 800 \text{ Rs} \]

### Final Answer
The total cost of painting all the cones is **Rs 800**.

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