The height of a conical tank is 60 cm and the diameter of its base is 64 cm. The cost of painting it from outside at the rate of Rs35 per sq m is

Options

A. Rs52.00 (approx)
B. Rs39.20 (approx)
C. Rs35.20 (approx)
D. Rs23.94 (approx)

Answer

To find the cost of painting the conical tank from the outside, we need to follow these steps:

### Step 1: Identify the dimensions of the cone
- Height (h) = 60 cm
- Diameter (d) = 64 cm
- Radius (r) = Diameter / 2 = 64 cm / 2 = 32 cm

### Step 2: Calculate the slant height (l) of the cone
The formula for the slant height of a cone is given by:
\[ l = \sqrt{r^2 + h^2} \]
Substituting the values:
\[ l = \sqrt{(32)^2 + (60)^2} \]
\[ l = \sqrt{1024 + 3600} \]
\[ l = \sqrt{4624} \]
\[ l = 68 \text{ cm} \]

### Step 3: Calculate the curved surface area (CSA) of the cone
The formula for the curved surface area of a cone is:
\[ \text{CSA} = \pi r l \]
Using \( \pi \approx 3.14 \):
\[ \text{CSA} = 3.14 \times 32 \times 68 \]
\[ \text{CSA} = 3.14 \times 2176 \]
\[ \text{CSA} \approx 6835.84 \text{ cm}^2 \]

### Step 4: Convert the area from cm² to m²
Since the cost is given per square meter, we need to convert the area:
\[ \text{Area in m}^2 = \frac{6835.84}{10000} = 0.683584 \text{ m}^2 \]

### Step 5: Calculate the cost of painting
The cost of painting is given by:
\[ \text{Cost} = \text{Area} \times \text{Rate} \]
Where the rate is Rs 35 per m²:
\[ \text{Cost} = 0.683584 \times 35 \]
\[ \text{Cost} \approx 23.43 \text{ Rs} \]

### Final Answer
The cost of painting the conical tank from outside is approximately Rs 23.43.

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