Question

In the given figure, the area of the shaded region is:
(Take π = 3.14)

[1 mark]

• A. 565.24 $c{m}^2$
• B. 575.24 $c{m}^2$
• C. 585.24 $c{m}^2$
• D. 595.24 $c{m}^2$

Answer 1

The correct option is A 565.24 $c{m}^2$

The figure can be broken down into 3 equal parts.
Let’s consider a section.


In one region, it has semicircles of diameter 6 cm and 16 cm.

Radius of small semicircle = $\frac{Diameter}{2}=\frac{6}{2}$ = 3 cm

Radius of big semicircle = $\frac{Diameter}{2}=\frac{16}{2}$ = 8 cm

Area of this shaded region = Area of large semicircle - Area of small semicircle
$=\frac{1}{2}\times \pi (8{)}^2-\frac{1}{2}\times \pi (3{)}^2=\frac{1}{2}\times \pi (64-9)=\frac{55}{2}\pi (cm{)}^2$

In another region, it has semicircles of diameters 8 cm and 18 cm.

Radius of small semicircle = $\frac{Diameter}{2}=\frac{8}{2}$ = 4 cm

Radius of big semicircle = $\frac{Diameter}{2}=\frac{18}{2}$ = 9 cm

Area of this shaded region = Area of large semicircle - Area of small semicircle
$=\frac{1}{2}\times \pi (9{)}^2-\frac{1}{2}\times \pi (4{)}^2=\frac{1}{2}\times \pi (81-16)=\frac{65}{2}\pi (cm{)}^2$

∴ Total shaded area of this section = $\pi \left(\frac{55+65}{2}\right)=60\pi c{m}^2$

Total shaded area of the figure
= 3 × 60π $c{m}^2$
= 180 × 3.14
= 565.24 $c{m}^2$