If the area of a semi-circle is `1925 cm^(2)`, then find its radius (in cm).

Options

A. 70
B. 31
C. 62
D. 35

Answer

To find the radius of a semi-circle given its area, we can follow these steps:

### Step 1: Understand the formula for the area of a semi-circle.
The area \( A \) of a semi-circle is given by the formula:
\[ A = \frac{1}{2} \pi r^2 \]
where \( r \) is the radius of the semi-circle.

### Step 2: Substitute the given area into the formula.
We know the area of the semi-circle is \( 1925 \, \text{cm}^2 \). Therefore, we can set up the equation:
\[ 1925 = \frac{1}{2} \pi r^2 \]

### Step 3: Solve for \( r^2 \).
First, multiply both sides of the equation by 2 to eliminate the fraction:
\[ 2 \times 1925 = \pi r^2 \]
\[ 3850 = \pi r^2 \]

### Step 4: Isolate \( r^2 \).
Next, divide both sides by \( \pi \):
\[ r^2 = \frac{3850}{\pi} \]

### Step 5: Calculate \( r \).
Now, take the square root of both sides to find \( r \):
\[ r = \sqrt{\frac{3850}{\pi}} \]

### Step 6: Substitute the value of \( \pi \) and calculate \( r \).
Using \( \pi \approx 3.14 \):
\[ r = \sqrt{\frac{3850}{3.14}} \approx \sqrt{1225} \approx 35 \]

### Conclusion
The radius of the semi-circle is approximately \( 35 \, \text{cm} \).

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