Question

A hemispherical bowl made of brass has inner diameter 10.5 cm. Find the cost of tin-plating it on the inside at the rate of ₹ 16 per 100 cm².

Answer 1

We are given the following information:

• Inner diameter of the hemispherical bowl = 10.5 cm
• Rate of tin-plating = ₹16 per 100 cm²

We are required to find the cost of tin-plating the inside of the bowl.

Step-by-Step Solution:

1. Formula for Surface Area of a Hemisphere:

The surface area \( A \) of a hemisphere (excluding the base) is given by the formula: \[ A = 2 \pi r^2 \] where \( r \) is the radius of the hemisphere.

2. Calculate the Radius of the Hemisphere:

The inner diameter of the hemisphere is 10.5 cm. Therefore, the radius \( r \) is: \[ r = \frac{\text{Diameter}}{2} = \frac{10.5}{2} = 5.25 \, \text{cm} \]

3. Calculate the Surface Area:

Now, we substitute the value of \( r = 5.25 \, \text{cm} \) into the formula for the surface area: \[ A = 2 \pi (5.25)^2 \] \[ A = 2 \pi \times 27.5625 \] Using \( \pi \approx 3.14 \), we get: \[ A = 2 \times 3.14 \times 27.5625 = 173.16 \, \text{cm}^2 \]

4. Calculate the Cost of Tin-Plating:

The cost of tin-plating is ₹16 per 100 cm². To find the cost for 173.16 cm², we use the following proportion: \[ \text{Cost} = \frac{16}{100} \times 173.16 = 27.74 \, \text{₹} \]

Final Answer:

The cost of tin-plating the inside of the hemispherical bowl is ₹ \(\boxed{27.74}\).