Question

The length of a rectangle is 16 cm which is 2 cm more than the diameter of a circle. What is the area of the circle?

• A. 154 sq. cm
• B. 176 sq.cm
• C. 112 sq.cm
• D. 136 sq.cm

Hint:

Diameter $d = 16 - 2 = 14\text{ cm} \implies r = 7\text{ cm} \implies \text{Area} = \frac{22}{7} \times 7^2 = 154\text{ sq. cm}$.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The area of a circle depends on its radius $r$ according to the geometric formula $A = \pi r^2$.

Step 2: Key Formula or Approach:
Length of rectangle $L = 16\,\text{cm}$.
Diameter of the circle $d = L - 2 = 16 - 2 = 14\,\text{cm}$.
Radius of the circle $r = \frac{d}{2} = \frac{14}{2} = 7\,\text{cm}$.

Step 3: Detailed Explanation:
Area of the circle:
\[A = \pi r^2 = \frac{22}{7} \times 7^2 = \frac{22}{7} \times 49 = 22 \times 7 = 154\,\text{cm}^2\]

Step 4: Final Answer:
Therefore, the area of the circle is 154 sq. cm.