Advertisements
Advertisements
Question
In the given figure, a square OABC has been inscribed in the quadrant OPBQ. If OA = 20 cm, then the area of the shaded region is
Options
214 cm2
228 cm2
242 cm2
248 cm2
Solution
228 cm2
Join OB.
Now, OB is the radius of the circle.
We have :
OB2 = OA + AB [By pythagoras' therom]
⇒ OB2 = {(20)2 + (20)2} cm2
⇒ OB2 =(400+400) cm2
⇒ OB2 = 800 cm2
`=> "OB" =20sqrt2 "cm"`
Hence, the radius of the circle is `20sqrt(2) "cm".`
Now,
Area of the shaded region = Area of the quadrant - Area of the square OABC\
`=|(1/4xx3.14xx20sqrt(2)xx20sqrt(2))-(20xx20)| "cm"^2`
`=|(1/4xx314/100xx800)-400| "cm"^2`
=(628-400) cm2
= 228 cm2
APPEARS IN
RELATED QUESTIONS
A lawn is in the form of a rectangle whose sides are in the ratio 5 : 3. The area of the lawn is `3375m^2` . Find the cost of fencing the lawn at ₹ 65 per metre.
What is the angle subtended at the centre of a circle of radius 6 cm by an arc of length 3 π cm?
If a chord of a circle of radius 28 cm makes an angle of 90 ° at the centre, then the area of the major segment is
A square is inscribed in a circle. Find the ratio of the areas of the circle and the square.
A child draws the figure of an aeroplane as shown. Here, the wings ABCD and FGHI are parallelograms, the tail DEF is an isosceles triangle, the cockpit CKI is a semicircle and CDFI is a square. In the given figure, BP ⊥ CD, HQ ⊥ FI and EL ⊥ DF. If CD = 8 cm, BP = HQ = 4 cm and DE = EF = 5 cm, find the area of the whole figure.
A round table cover has six equal designs as shown in the given figure. If the radius of the cover is 35 cm, then find the total area of the design.
The length of the minute hand of a clock is 21 cm. The area swept by the minute hand in 10 minutes is
The area of a sector of a circle with radius r, making an angle of x° at the centre is
The diameter of a wheel is 0.70 m. Find the distance covered by it in 500 revolutions. If the wheel takes 5 minutes to make 500 revolutions; find its speed in :
(i) m/s
(ii) km/hr.
A 7m wide road surrounds a circular garden whose area is 5544m2. Find the area of the road and the cost of tarring it at the rate of Rs.150 per m2.
