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Question
In the given figure, ABCD is a rectangle inscribed in a circle having length 8 cm and breadth 6 cm. If π = 3.14, then the area of the shaded region is:
Options
264 cm2
266 cm2
272 cm2
254 cm2
None of the above.
Solution
None of the above
Explanation:
All options are incorrect; the correct answer is 30.5 cm.
Join AC.
Now, AC is the diameter of the circle.
We have:
AC2 = AB2 + BC2 [By pythagoras' theorem]
⇒ AC2 = {(8)2 + (6)2} cm2
⇒ AC2 = (64 + 36) cm2
⇒ AC2 = 100 cm2
∴ Radius of the circle`=10/2 "cm"`
= 5 cm
Now,
Area of the shaded region = Area of the circle with radius 5 cm − Area of the rectangle ABCD
`=|(3.14xx5xx5)-(8xx6)| "cm"^2`
`=|(314/100xx25)-48| "cm"^2`
`=(157/2-48) "cm" ^2`
`=61/2 "cm" ^2`
= 30.5 cm2
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