If the circumference of a circle is 22 cm, find the area of the semicircle.
A. 38.5 sq.cm
B. 19.25 sq.cm
C. 44 sq.cm
D. 77 sq.cm

Options

A. A
B. D
C. C
D. B

Answer

To find the area of a semicircle given that the circumference of the circle is 22 cm, we can follow these steps:

### Step 1: Use the formula for the circumference of a circle
The formula for the circumference (C) of a circle is given by:
\[ C = 2\pi r \]
where \( r \) is the radius of the circle.

### Step 2: Set the circumference equal to 22 cm
Given that the circumference is 22 cm, we can set up the equation:
\[ 2\pi r = 22 \]

### Step 3: Solve for the radius (r)
To find the radius, we can rearrange the equation:
\[ r = \frac{22}{2\pi} \]
Substituting \( \pi \) with \( \frac{22}{7} \) (an approximation for calculations):
\[ r = \frac{22}{2 \times \frac{22}{7}} \]
\[ r = \frac{22 \times 7}{44} = \frac{7}{2} \text{ cm} \]

### Step 4: Calculate the area of the circle
The area (A) of a circle is given by the formula:
\[ A = \pi r^2 \]
Substituting the radius we found:
\[ A = \pi \left(\frac{7}{2}\right)^2 \]
\[ A = \pi \times \frac{49}{4} \]
Using \( \pi \approx \frac{22}{7} \):
\[ A = \frac{22}{7} \times \frac{49}{4} \]
\[ A = \frac{22 \times 49}{28} = \frac{1078}{28} = 38.5 \text{ cm}^2 \]

### Step 5: Calculate the area of the semicircle
The area of a semicircle is half of the area of the circle:
\[ \text{Area of semicircle} = \frac{A}{2} = \frac{38.5}{2} = 19.25 \text{ cm}^2 \]

### Conclusion
The area of the semicircle is \( 19.25 \text{ cm}^2 \).

### Answer
B. 19.25 sq.cm