Advertisements
Advertisements
प्रश्न
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
विकल्प
214 cm2
228 cm2
242 cm2
248 cm2
उत्तर
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
संबंधित प्रश्न
A road which is 7 m wide surrounds a circular park whose circumference is 352 m . Find the area of the road .
A square water tank has its side equal to 40 m. There are four semi-circular grassy plots all round it. Find the cost of turfing the plot at Rs. 1.25 per square metre (Take π = 3.14).
In a circle of radius 10 cm, an arc subtends an angle of 108° at the centre. what is the area of the sector in terms of π?
If a square is inscribed in a circle, what is the ratio of the areas of the circle and the square?
The area of a circle whose area and circumference are numerically equal, is
The radii of two circles are 8 cm and 6 cm. Find the radius of the circle having area equal to the sum of the areas of the two circles.
On decreasing the radius of a circle by 30%, its area is decreased by
A chord of a circle of radius 14 cm a makes a right angle at the centre. Find the area of the sector.
A lawn is in the shape of a semicircle of diameter 42m. the lawn is surrounded by a flower bed of width 7m all round. Find the area of the flower bed in m2.
The circumference of a circular park is 352 m. Find the area of the park
