A hemispherical bowl has 3.5 cm radius. It is to be painted inside as well as outside. The cost of painting it at the rate of Rs. 5 per 10 sq. cm will be :

Options

A. Rs. 77
B. Rs. 100
C. Rs. 175
D. Rs. 50

Answer

To find the cost of painting a hemispherical bowl with a radius of 3.5 cm, we need to calculate the total surface area that needs to be painted (both inside and outside) and then determine the cost based on the given rate.

### Step-by-Step Solution:

1. **Identify the radius of the hemispherical bowl**:
- Given radius \( r = 3.5 \) cm.

2. **Calculate the surface area of the hemispherical bowl**:
- The formula for the total surface area of a hemispherical bowl (including the base) is:
\[ \text{Total Surface Area} = 3\pi r^2 \]
- Here, \( \pi \) can be approximated as \( \frac{22}{7} \).

3. **Substitute the radius into the formula**:
- First, calculate \( r^2 \):
\[ r^2 = (3.5)^2 = 12.25 \text{ cm}^2 \]
- Now substitute \( r^2 \) into the surface area formula:
\[ \text{Total Surface Area} = 3 \times \frac{22}{7} \times 12.25 \]

4. **Calculate the total surface area**:
- First, calculate \( 3 \times 12.25 = 36.75 \).
- Now calculate:
\[ \text{Total Surface Area} = \frac{22 \times 36.75}{7} \]
- Calculate \( 22 \times 36.75 = 810.5 \).
- Now divide by 7:
\[ \text{Total Surface Area} = \frac{810.5}{7} \approx 115.7857 \text{ cm}^2 \]

5. **Calculate the cost of painting**:
- The cost of painting is given as Rs. 5 per 10 sq. cm.
- First, find the cost per sq. cm:
\[ \text{Cost per cm}^2 = \frac{5}{10} = 0.5 \text{ Rs.} \]
- Now, multiply the total surface area by the cost per sq. cm:
\[ \text{Total Cost} = 115.7857 \times 0.5 \approx 57.89285 \text{ Rs.} \]

6. **Round the total cost**:
- Rounding to the nearest whole number, the total cost is approximately Rs. 58.

### Final Answer:
The cost of painting the hemispherical bowl is approximately **Rs. 58**.

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