Question

A hemispherical bowl is made of steel, 0.25 cm thick. The inner radius of the bowl is 5 cm. Find the outer curved surface area of the bowl.

Answer 1

We are given a hemispherical bowl with the following details:

• Inner radius of the bowl = 5 cm
• Thickness of the bowl = 0.25 cm

We need to find the outer curved surface area of the bowl.

Step-by-Step Solution:

1. Understanding the Problem:

The bowl is hemispherical, so it has a circular base and a curved surface. The thickness of the bowl is given as 0.25 cm, and the inner radius is 5 cm. Therefore, the outer radius will be: \[ \text{Outer radius} = \text{Inner radius} + \text{Thickness} = 5 \, \text{cm} + 0.25 \, \text{cm} = 5.25 \, \text{cm} \]

2. Formula for Curved Surface Area of a Hemisphere:

The formula for the curved surface area (CSA) of a hemisphere is given by: \[ \text{CSA} = 2 \pi r^2 \] where \( r \) is the radius of the hemisphere.

3. Find the Outer Curved Surface Area:

Using the outer radius \( r = 5.25 \, \text{cm} \), we can calculate the outer curved surface area: \[ \text{CSA} = 2 \pi (5.25)^2 \] \[ \text{CSA} = 2 \pi \times 27.5625 = 55.125 \pi \, \text{cm}^2 \] Substituting \( \pi \approx 3.14 \): \[ \text{CSA} = 55.125 \times 3.14 = 172.52 \, \text{cm}^2 \]

Final Answer:

The outer curved surface area of the hemispherical bowl is \( \boxed{172.52 \, \text{cm}^2} \).