A semicircle of radius 17.5 cm is ratiatied about its diameter. Find the curved surface of so generated solid

Explanation

To find the curved surface area of the solid generated by rotating a semicircle about its diameter, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the radius of the semicircle**:
Given that the radius \( r \) of the semicircle is \( 17.5 \) cm.

2. **Calculate the diameter**:
The diameter \( d \) of the semicircle can be calculated using the formula:
\[ d = 2r \]
Substituting the value of \( r \):
\[ d = 2 \times 17.5 = 35 \text{ cm} \]

3. **Understand the shape formed**:
When the semicircle is rotated about its diameter, it forms a solid known as a hemisphere.

4. **Curved surface area formula**:
The formula for the curved surface area \( A \) of a hemisphere is given by:
\[ A = 2\pi r^2 \]

5. **Substitute the radius into the formula**:
We substitute \( r = 17.5 \) cm into the formula:
\[ A = 2 \pi (17.5)^2 \]

6. **Calculate \( (17.5)^2 \)**:
\[ (17.5)^2 = 306.25 \]

7. **Substitute back into the area formula**:
\[ A = 2 \pi \times 306.25 \]
\[ A = 612.5 \pi \]

8. **Use \( \pi \approx \frac{22}{7} \) for calculation**:
\[ A \approx 612.5 \times \frac{22}{7} \]

9. **Calculate the area**:
\[ A \approx 612.5 \times 3.14 \approx 1925.625 \text{ cm}^2 \]

10. **Final Result**:
The curved surface area of the solid generated by rotating the semicircle about its diameter is approximately:
\[ A \approx 1925.63 \text{ cm}^2 \]