Question

If the radius of a circle is increased by 20%, what is the percentage increase in the area?

• A. 400%
• B. 40%
• C. 44%
• D. 144%

Hint:

Area increases by the square of the radius multiplier: \((1.2)^2 = 1.44\), so increase is 44%.

Answer 1

The Correct Option is C

Original area: \[ A = \pi r^2 \] New radius = \(1.2r\) New area: \[ A' = \pi (1.2r)^2 = \pi \cdot 1.44r^2 \] Percentage increase: \[ \frac{A' - A}{A} \times 100 = \frac{1.44A - A}{A} \times 100 = 0.44 \times 100 = \boxed{44%} \]