Advertisements
Advertisements
प्रश्न
The radii of two circles are in the ratio 5 : 8. If the difference between their areas is 156p cm2, find the area of the bigger circle.
Advertisements
उत्तर
Let r1 and r2 be the radii of two circles.
⇒ r1 : r2 = 5:8
⇒`"r"_1/"r"_2 = (5)/(8)`
⇒ r1 = `(5)/(8)"r"_2`
It is given that,
πr22 - πr12 = 156π
⇒ r22 - r12 = 156
⇒ `"r"_2^2 - (5/8"r"_1)^2` = 156
⇒ `"r"_2^2 - (25)/(64)"r"_2^2` = 156
⇒ `(64"r"_2^2 - 25"r"_2^2)/(64)` = 156
⇒ 39r22 = 64 x 156
⇒ r22 = `(64 xx 156)/(39)` = 256
⇒ r2 = 16
∴ Area of bigger circle
= πr22
= `(22)/(7) xx 16 xx 16`
= 804.57cm2.
APPEARS IN
संबंधित प्रश्न
The length of a rectangular park is twice its breadth and its perimeter is 840 m. Find the area of the park.
Find the area of minor segment of a circle of radius 14 cm, when the angle of the corresponding sector is 600 .
ABCDEF is a regular hexagon with centre O (in the following figure). If the area of triangle OAB is 9 cm2, find the area of : (i) the hexagon and (ii) the circle in which the haxagon is incribed.
If a wire is bent into the shape of a square, then the area of the square is 81 cm2. When wire is bent into a semi-circular shape, then the area of the semi-circle will be ______.
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.
A pendulum swings through an angle of 30° and describes an arc 8.8 cm in length. Find the length of the pendulum.
If a square is inscribed in a circle, find the ratio of the areas of the circle and the square.
On decreasing the radius of a circle by 30%, its area is decreased by
Find the radius and circumference of a circle, whose area is :
(i) 154 cm2
(ii) 6.16 m2
A circular field of radius 105 m has a circular path of uniform width of 5 m along and inside its boundary. Find the area of the path.
