Question

In figure , BC is a diameter of the circle, AC = 6cm and AB = 8 cm. Find the area of the shaded region. (use $\pi =3.14$)

• A. $36c{m}^2$
• B. $44.5c{m}^2$
• C. $54.5c{m}^2$
• D. $50c{m}^2$

Answer 1

The correct option is C

$54.5c{m}^2$

Given: AC = 6 cm and AB = 8cm

We know that, angle in a semi circle is ${90}^{\circ }$.

$\therefore \angle A={90}^{\circ }$

In right angled $\Delta ACB$, use Pythagoras Theorem

$\therefore B{C}^2=A{C}^2+B{A}^2$

$\Rightarrow B{C}^2=6^2+8^2=36+64$

$\Rightarrow B{C}^2=100$

$\Rightarrow BC=10cm$

$\therefore$ Area of $\Delta ABC=\frac{1}{2}\times AB\times AC=\frac{1}{2}\times 8\times 6=24c{m}^2$

Here, diameter of circle, AB = 10 cm

Radius of circle $r=\frac{10}{2}=5cm$

Area of circle $=\pi r^2=3.14\times (5{)}^2$

$=3.14\times 25=78.5c{m}^2$

Area of the shaded region = Area of circle - Area of $\Delta ABC$

$78.5-24=54.5c{m}^2$