Question

The ratio of total area of the rectangle to the total shaded area

• A. $\frac{2}{\pi }$
• B. $\frac{4}{4-\pi }$
• C. $\frac{4-\pi }{\pi }$
• D. $\frac{\pi }{4}$

Answer 1

The correct option is B $\frac{4}{4-\pi }$

Let the radius of circle be $r$

Then sides of rectangle are $2r$ and $4r$.

Area of rectangle $=2r\times 4r=8r^2$

Area of circles$=2\times \left(\pi r^2\right)=2\pi r^2$

Hence area of shaded region$=8r^2-2\pi r^2=2r^2(4-\pi )$

So,,

$\frac{A_{rect}}{A_{shaded}}=\frac{8r^2}{2r^2(4-\pi )}=\frac{4}{4-\pi }$