Question

In the given figure below, the boundary of the shaded region comprises of four semicircles and two quarter cirles. If $OA=OB=OC=OD=7cm$ and the straight lines $AC$ and $BD$ are perpendicular to each other, then the length of the boundary is

• A. $68cm$
• B. $49cm$
• C. $66cm$
• D. $44cm$

Answer 1

Answer: (C)

$66cm$

$OA=OB=OC=OD=7cm$

Circumference of semicircle$=\pi r$

Here, we have four semicircles with radius $\frac{7}{2}$cm.

Then, circumference of these for semicircles

$=4\times \pi r$

$=4\times \frac{22}{7}\times \frac{7}{2}$

$=44cm$

$\therefore$ We have two quarter circle with radius $7cm$.

Then, circumference of these two quarter circle:

$=2\times \frac{\pi r}{2}$

$=\frac{22}{7}\times 7$

$=22cm$

$\therefore$ Length of boundary of shaded region$=44+22$

$=66cm$.