If the radius of a circle is increased by 200%, then its area will increase by :

Answer: Option C

Let the original radius be R
New radius = (100 + 200)% of R = 300% of R = 3R
Original area = $$\pi$$R²
New area = $$\pi$$ × (3R)² = 9$$\pi$$R²
Increase in area :
$$\begin{array}{rl}& =\left(9\pi {\text{R}}^2-\pi {\text{R}}^2\right)\\ & =8\pi {\text{R}}^2\end{array}$$
∴ Increase %:
$$\begin{array}{rl}& =\left(\frac{8\pi {\text{R}}^2}{\pi {\text{R}}^2}\times 100\right)\%\\ & =800\%\end{array}$$