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.
Advertisements
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
One side of a rectangle is 12 cm long and its diagonal measure 37 cm. Find the other side and the area of the rectangle.
Two concentric circles of radii a and b (a > b) are given. Find the length of the chord of the larger circle which touches the smaller circle.
AB is a chord of a circle with centre O and radius 4 cm. AB is of length 4 cm. Find the area of the sector of the circle formed by chord AB.
In the following figure, there are three semicircles, A, B and C having diameter 3 cm each, and another semicircle E having a circle D with diameter 4.5 cm are shown. Calculate:
(i) the area of the shaded region
(ii) the cost of painting the shaded region at the rate of 25 paise per cm2 , to the nearest rupee.
In the following figure, shows the cross-section of railway tunnel. The radius OA of the circular part is 2 m. If ∠AOB = 90°, calculate:
the perimeter of the cross-section
Write the area of the sector of a circle whose radius is r and length of the arc is l.
The ratio of the outer and inner perimeters of a circular path is 23 : 22. If the path is 5 metres wide, the diameter of the inner circle is
From a thin metallic piece in the shape of a trapezium ABCD in which AB || CD and ∠BCD = 90°, a quarter circle BFEC is removed. Given, AB = BC = 3.5 cm and DE = 2 cm, calculate the area of remaining (shaded) part of metal sheet.
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.
Is the area of the largest circle that can be drawn inside a rectangle of length a cm and breadth b cm (a > b) is πb2 cm2? Why?
