Question

Find the area of shaded region, if AC and BC are diameters of length 28 cm and 14 cm respectively.

• A. 77 $c{m}^2$
• B. 154 $c{m}^2$
• C. 231 $c{m}^2$
• D. 462 $c{m}^2$

Answer 1

The correct option is C 231 $c{m}^2$

R = radius of larger semicircle
= $\frac{AC}{2}$ = $\frac{28}{2}$ = 7 cm

r = radius of smaller semicircle
= $\frac{BC}{2}$ = $\frac{14}{2}$ = 14 cm

(Since radius of a circle = $\frac{diameter}{2}$)

Area of shaded region =
Area of semicircle with diameter AC - Area of semicircle with diameter BC

Area of a semicircle = $\frac{1}{2}$$\times$$\pi$$(radius{)}^2$

Area of semicircle having diameter BC = $\frac{1}{2}$$\times$$\pi$$\times$$r^2$ = $\frac{1}{2}$$\times$$\frac{22}{7}$$\times$$7^2$ = 77 $c{m}^2$

Area of semicircle having diameter AC = $\frac{1}{2}$$\times$$\pi$$\times$$R^2$ = $\frac{1}{2}$$\times$$\frac{22}{7}$$\times$${14}^2$
= 11$\times$28 = 308 $c{m}^2$

Area of shaded region = 308 - 77 = 231 $c{m}^2$