Answer :
To find the area of the semicircle, we first need to find the radius of the circle using the given circumference. Once we have the radius, we can calculate the area of the circle and then find the area of the semicircle, which is half of the circle's area. Here's how you can solve it step-by-step:
1. Find the Radius:
- The formula for the circumference (C) of a circle is [tex]\( C = 2 \pi r \)[/tex], where [tex]\( r \)[/tex] is the radius.
- We are given that the circumference is 176 cm.
- Rearrange the formula to solve for the radius:
[tex]\[
r = \frac{C}{2\pi} = \frac{176}{2\pi} \approx 28.01 \text{ cm}
\][/tex]
2. Calculate the Area of the Circle:
- The formula for the area [tex]\( A \)[/tex] of a circle is [tex]\( A = \pi r^2 \)[/tex].
- Substitute the radius into the formula to find the area:
[tex]\[
A = \pi \times (28.01)^2 \approx 2464.99 \text{ cm}^2
\][/tex]
3. Find the Area of the Semicircle:
- The area of a semicircle is half the area of the entire circle.
- So, calculate the semicircle's area:
[tex]\[
\text{Area of the semicircle} = \frac{2464.99}{2} \approx 1232.50 \text{ cm}^2
\][/tex]
Therefore, the area of the semicircle is approximately 1232.50 cm².
1. Find the Radius:
- The formula for the circumference (C) of a circle is [tex]\( C = 2 \pi r \)[/tex], where [tex]\( r \)[/tex] is the radius.
- We are given that the circumference is 176 cm.
- Rearrange the formula to solve for the radius:
[tex]\[
r = \frac{C}{2\pi} = \frac{176}{2\pi} \approx 28.01 \text{ cm}
\][/tex]
2. Calculate the Area of the Circle:
- The formula for the area [tex]\( A \)[/tex] of a circle is [tex]\( A = \pi r^2 \)[/tex].
- Substitute the radius into the formula to find the area:
[tex]\[
A = \pi \times (28.01)^2 \approx 2464.99 \text{ cm}^2
\][/tex]
3. Find the Area of the Semicircle:
- The area of a semicircle is half the area of the entire circle.
- So, calculate the semicircle's area:
[tex]\[
\text{Area of the semicircle} = \frac{2464.99}{2} \approx 1232.50 \text{ cm}^2
\][/tex]
Therefore, the area of the semicircle is approximately 1232.50 cm².
