Question

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

• A. 400 %
• B. 40 %
• C. 44 %
• D. 144 %

Hint:

When the radius of a circle is increased, the area increases by the square of the factor by which the radius is increased.

Answer 1

The Correct Option is C

To determine the percentage increase in the area of a circle when its radius is increased by 20%, follow these steps:

1. Let the original radius of the circle be \( r \).
2. The original area of the circle is given by the formula: \[ A = \pi r^2 \]
3. When the radius is increased by 20%, the new radius becomes: \[ r_{\text{new}} = r + 0.2r = 1.2r \]
4. The new area of the circle with the increased radius is: \[ A_{\text{new}} = \pi (1.2r)^2 = \pi \times 1.44r^2 \]
5. The change in area can be calculated as: \[ \Delta A = A_{\text{new}} - A = \pi \times 1.44r^2 - \pi r^2 = 0.44\pi r^2 \]
6. The percentage increase in the area is: \[ \left(\frac{\Delta A}{A}\right) \times 100\% = \left(\frac{0.44\pi r^2}{\pi r^2}\right) \times 100\% = 44\% \]

Therefore, the percentage increase in the area of the circle is 44%.