Question

In the figure the boundary of the shaded region consists of four 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
1 . The length of the boundary
2 . The area of the shaded region

Answer 1

1. Length of the boundary

Length of the boundary=perimeter of semi circle with diameter $AB$ boundary of semi circle with diameter $7cm$

Length of boundary $=(\pi \times 7+\pi \times 3.5)+\pi \times 1.75+\pi \times 1.75$

Length of boundary $=\pi (7+3.5+1.75+1.75)$

$=44cm$

$\therefore$ The length of the boundary is $44cm$.

2.Area of shaded region =

Area of largest semicircle + Area of medium semicircle-2 (Area of small semicircle )

$Area=\frac{22}{7}\times \frac{7\times 7}{2}+\frac{22}{7}\times \frac{35}{100}\times \frac{35}{2}-2(\frac{22}{7}-\frac{175\times 175}{100\times 100})$

$=77+19.25-2\left(481\right)$

$=96.25-9.62$

$=86.63c{m}^2$

Area of shaded region $=86.63c{m}^2$