Advertisements
Advertisements
Question
The sum of the radii of two circles is 10.5 cm and the difference of their circumferences is 13.2 cm. Find the radii of the two circles.
Solution
Let r1 and r2 be the radii of two circles.
⇒ r1 + r2 = 10.5 ....(i)
And,
`2π"r"_(6.3-4.21) - 2π"r"_2` = 13.2
⇒ `2 xx (22)/(7) xx ("r"_1 - "r"_2)` = 13.2
⇒ r1 - r2 = `(13.2 xx 7)/(2 xx 22)`
⇒ r1 - r2 = 2.1 ....(ii)
Adding (i) and (ii), we get
2r1 = 12.6
⇒ r1 = 6.3cm
Now,
r1 - r2 = 2.1
⇒ 6.3 - r2 = 2.1
⇒ r2 = 4.2cm.
APPEARS IN
RELATED QUESTIONS
Find the cost of polishing a circular table-top of diameter 1.6 m, if the rate of polishing is ₹ 15/m2. (Take π = 3.14)
The hour hand of a clock is 6 cm long. The area swept by it between 11.20 am and 11.55 am is
Find the area of a ring whose outer and inner radii are respectively 23 cm and 12 cm.
A rope by which a cow is tethered is increased from 16 m to 23 m. How much additional ground does it have now graze?
In the given figure, O is the centre of the circle with AC = 24 cm, AB = 7 cm and ∠BOD = 90°. Find the area of shaded region.
In the given figure, ∆ABC is right-angled at A. Semicircles are drawn on AB, AC and BC as diameters. It is given that AB = 3 cm and AC = 4 cm. Find the area of the shaded region.
A circle of the largest area is cut from a rectangular piece of cardboard with dimensions 55 cm and 42 cm. Find the ratio between the area of the circle cut and the area of the remaining card-board.
A wire, when bent in the form of a square; encloses an area of 196 cm2. If the same wire is bent to form a circle; find the area of the circle.
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.
If the radii of two circles are in the ratio of 4 : 3, then their areas are in the ratio of ______.
