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.

Explanation

To find the outer curved surface area of a hemispherical bowl made of steel with a thickness of 0.25 cm and an inner radius of 5 cm, we can follow these steps:

### Step 1: Determine the Outer Radius
The outer radius (R) of the hemispherical bowl can be calculated by adding the thickness of the bowl to the inner radius.

\[ R = \text{Inner Radius} + \text{Thickness} \]
\[ R = 5 \, \text{cm} + 0.25 \, \text{cm} = 5.25 \, \text{cm} \]

### Step 2: Use the Formula for the Curved Surface Area of a Hemisphere
The formula for the curved surface area (CSA) of a hemisphere is given by:

\[ \text{Curved Surface Area} = 2 \pi R^2 \]

### Step 3: Substitute the Outer Radius into the Formula
Now, substitute the value of R into the formula. We can use \( \pi \approx \frac{22}{7} \) for our calculations.

\[ \text{Curved Surface Area} = 2 \times \frac{22}{7} \times (5.25)^2 \]

### Step 4: Calculate \( (5.25)^2 \)
First, calculate \( (5.25)^2 \):

\[ (5.25)^2 = 27.5625 \]

### Step 5: Substitute and Calculate the Curved Surface Area
Now substitute \( (5.25)^2 \) back into the formula:

\[ \text{Curved Surface Area} = 2 \times \frac{22}{7} \times 27.5625 \]

Calculating this step-by-step:

1. Multiply \( 2 \times \frac{22}{7} \):
\[ = \frac{44}{7} \]

2. Now multiply by \( 27.5625 \):
\[ \text{Curved Surface Area} = \frac{44 \times 27.5625}{7} \]

3. Calculate \( 44 \times 27.5625 = 1216.75 \)

4. Finally, divide by 7:
\[ \text{Curved Surface Area} = \frac{1216.75}{7} \approx 173.25 \, \text{cm}^2 \]

### Final Answer
The outer curved surface area of the hemispherical bowl is approximately \( 173.25 \, \text{cm}^2 \).

---