Question

In the given figure the boundary of the shaded region consists of 4 semicircular arcs, the smallest two being equal. If the diameter of the largest is 14 cm and of the smallest is 3.5 cm, find the length of the boundary.

Answer 1

Length of boundary = Total circumference

Largest semicircle has diameter as $14$ cm

$\therefore$ radius = $\frac{D}{2}=\frac{Kp}{2}=7cm$

Circumference = $\pi r$

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

Circumference semi circle with E as centre is same as circumface of semicircle with C as centre

$\therefore$ circumference of = $\pi r$

$I^{st}$ circle + $I{I}^{nd}$ circle = $\frac{22}{7}\times \left(3.5\right)$

$=11cm$

Circumference of semi circle with $7cm$ diameter

$=\pi r$

$=\frac{22}{7}\times \frac{7}{2}=11$

$\therefore$ Total circumference = $22+11+11=44cm$