Question

Two concentric circles have radii $10$ and $8$. If the radius of the outer circle in increased by $10$% and the radius of the inner circle is decreased by $50$%, find the percentage increase in the area of the region enclosed by the circle.

• A. $102\pi$
• B. $103\pi$
• C. $104\pi$
• D. $105\pi$

Answer 1

The correct option is D $105\pi$

Let $r_1=10cm,r_2=8cm$

Area enclosed = Area of bigger circle – Area of smaller circle

$=\pi r_1^2–\pi r_2^2$

$=\pi (100-64)=36\pi$

Now

$R_1=r_1+\frac{10}{100}{r}_1$

$R_2=r_2-\frac{50}{100}{r}_2$

$⟹R_1=1.1r_1,R_2=\frac{r_2}{2}$

Area enclosed $=\pi R_1^2–\pi R_2^2$

$=\pi (1.21r_1^2-\frac{r_2^2}{4})$

$=\pi (121-16)=105\pi$