Question

The area of a circle is 154 cm². What is its radius? (Use \( \pi = \frac{22}{7} \))

• A. 5 cm
• B. 6 cm
• C. 7 cm
• D. 8 cm

Hint:

Solve \( \pi r^2 = \text{Area} \) and simplify fractions to find the radius.

Answer 1

The Correct Option is C

We need the radius of the circle.
- Step 1: Recall area formul(a) Area = \( \pi r^2 \). Given area = 154 cm², \( \pi = \frac{22}{7} \).
- Step 2: Set up equation.
\[ \frac{22}{7} r^2 = 154 \] - Step 3: Solve for \( r^2 \).
\[ r^2 = 154 \times \frac{7}{22} = \frac{154 \times 7}{22} = \frac{1078}{22} = 49 \] - Step 4: Find radius.
\[ r = \sqrt{49} = 7 \] - Step 5: Verify. Area = \( \frac{22}{7} \times 7^2 = \frac{22}{7} \times 49 = 154 \). Correct.
- Step 6: Check options.
- (a) 5: \( \frac{22}{7} \times 25 \approx 78.57 \neq 154 \).
- (b) 6: \( \frac{22}{7} \times 36 \approx 113.14 \neq 154 \).
- (c) 7: Correct.
- (d) 8: \( \frac{22}{7} \times 64 \approx 201.14 \neq 154 \).
- Step 7: Alternative check. Circumference test later if needed, but area confirms.
Thus, the answer is c.