Question

The adjacent figure consists of four half circles and two quarter circles. If $OA=OB=OC=OD=14cm$. Find the area of the shaded region.

• A. $457.34c{m}^2$
• B. $307.88c{m}^2$
• C. $667.67c{m}^2$
• D. $566.05c{m}^2$

Answer 1

The correct option is B $307.88c{m}^2$

Given: $OA=OB=OC=OD=14cm.$

Area of shaded region$=2\times$(Area of arc ODB+Area of semi-circle OD-Area of semi-circle OB)

$=2\times (\pi \times {14}^2\times \frac{90}{360}+\frac{\pi \times 7^2}{2}-\frac{\pi \times 7^2}{2})$

$=\frac{2\times \pi \times {14}^2}{4}=98\pi =307.88c{m}^2$