Question

In the given figure, a rectangle $OABC$ is inscribed in a quadrant $OPBQ$. If $AB=8\text{cm}$ and $BC=6\text{cm}$, then area of shaded region is equal to (Use $\pi =3.14$)

• A. $48{\text{cm}}^2$
• B. $24{\text{cm}}^2$
• C. $50.24{\text{cm}}^2$
• D. $30.5{\text{cm}}^2$

Answer 1

The correct option is D $30.5{\text{cm}}^2$

Given : $AB=8\text{cm},BC=6\text{cm}$
In $\Delta OCB,BC\perp OC$

By Pythagoras theorem,
$\Rightarrow O{B}^2=B{C}^2+O{C}^2$
$\Rightarrow O{B}^2=6^2+8^2$ $(\because OC=AB)$
$\Rightarrow O{B}^2=\sqrt{36+64}=10\text{cm}$

$\therefore$ Area of shaded region $=$ Area of quadrant $POQ–$ Area of rectangle $OABC$
$=\frac{1}{4}\times \pi \times {10}^2-8\times 6$
$=(25\pi -48){\text{cm}}^2$
$=30.5{\text{cm}}^2$
Hence, the correct answer is option d.