Question

In Fig. the boundary of the shaded region consists of four semi-circular arcs, the smallest two being equal. If the diameter of the largest is 14 cm and of the smallest is 3.5 cm, find

(i) The length of the boundary

(ii) The area of the shaded region.

Answer 1

Diameter of biggest semi circle = 14cm.
Diameter to two small semi circle = 3.5cm.
Diameter of other semi circle = 14-(2$times$3.5) = 7cm.
Area of biggest semi circle = $\frac{1}{2}\times \pi \times 7^{2}c{m}^2$
Area of two small semi circle = $\pi \times {1.75}^{2}c{m}^2$
Area of other semi circle = $\frac{1}{2}\times \pi \times {3.5}^{2}c{m}^2$
Area of shaded region
= $\pi \times (24.5-3.0625+12.25)$
= $\pi \times 27.5625c{m}^2=86.59c{m}^2$