In a building , there are 24 cyclinder pillars , For each pillar , radius is 28 cm and height is 4m . Find the total cost to painting the curved surface area of the pillars at the rate of ` 8 " per " m^(2) `

Answer

To solve the problem step-by-step, we will calculate the total cost to paint the curved surface area of the 24 cylindrical pillars.

### Step 1: Understand the given data
- Number of pillars = 24
- Radius of each pillar = 28 cm
- Height of each pillar = 4 m

### Step 2: Convert the radius into meters
Since the radius is given in centimeters, we need to convert it into meters for consistency with the height.
- Radius in meters = 28 cm ÷ 100 = 0.28 m

### Step 3: Calculate the curved surface area (CSA) of one pillar
The formula for the curved surface area of a cylinder is:
\[ \text{CSA} = 2 \pi r h \]
Substituting the values:
- \( r = 0.28 \, \text{m} \)
- \( h = 4 \, \text{m} \)

Using \( \pi \approx \frac{22}{7} \):
\[ \text{CSA} = 2 \times \frac{22}{7} \times 0.28 \times 4 \]

### Step 4: Simplify the calculation
Calculating step-by-step:
1. Calculate \( 2 \times \frac{22}{7} = \frac{44}{7} \)
2. Calculate \( 0.28 \times 4 = 1.12 \)
3. Now multiply:
\[ \text{CSA} = \frac{44}{7} \times 1.12 \]

### Step 5: Calculate the CSA in square meters
To calculate \( \frac{44 \times 1.12}{7} \):
1. \( 44 \times 1.12 = 49.28 \)
2. Now divide by 7:
\[ \text{CSA} = \frac{49.28}{7} \approx 7.04 \, \text{m}^2 \]

### Step 6: Calculate the total CSA for 24 pillars
Total CSA for 24 pillars:
\[ \text{Total CSA} = 24 \times 7.04 \]
\[ \text{Total CSA} = 169.04 \, \text{m}^2 \]

### Step 7: Calculate the total cost for painting
The cost to paint is given as Rs. 8 per m²:
\[ \text{Total Cost} = \text{Total CSA} \times \text{Rate} \]
\[ \text{Total Cost} = 169.04 \times 8 \]
\[ \text{Total Cost} = 1352.32 \]

### Final Answer
The total cost to paint the curved surface area of the pillars is approximately Rs. 1352.32.

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