In the given figure, ABCD is a rectangle inscribed in a circle ha… - Vidyadip

MCQ

In the given figure, $\text{ABCD}$ is a rectangle inscribed in a circle having length $8 \ cm$ and breadth $6 \ cm$. If $\pi=3.14$ then the area of the shaded region is:

A
$264\ cm^2$
B
$266\ cm^2$
C
$272\ cm^2$
✓
None of the above

✓

Answer

Correct option: D.

None of the above

Join $AC$.
Now, $AC$ is the diameter of the circle.
We have:
$AC^2 = AB^2 + BC^2 [$By pythagoras' theorem$]$
$\Rightarrow\text{AC}^2=\big\{(8)^2+(6)^2\big\}\text{cm}^2$
$\Rightarrow\text{AC}^2=(64+36)\text{cm}^2$
$\Rightarrow\text{AC}^2=100\text{cm}^2$
$\Rightarrow\text{AC}=10\text{cm}$
$\therefore$ Radius of the circle $=\frac{10}{2}\text{cm}$
$=5\text{cm}$
Now,
Area of the shaded region $=$ Area of the circle with radius $5\ cm -$ Area of the rectangle $\text{ABCD}$
$=\big|(3.14\times5\times5)-(8\times6)\big|\text{cm}^2$
$=\Big|\Big(\frac{314}{100}\times25\Big)-48\Big|\text{cm}^2$
$=\Big(\frac{157}{2}-48\Big)\text{cm}^2$
$=\frac{61}{2}\text{cm}^2$
$=30.5\text{cm}^2$

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