The sum of the radii of two circles is 140 cm and the difference of their circumferences is 88 cm. Find the diameters of the circles.
Answers
Answer :
The diameter of the circles are 154 cm & 126 cm.
SOLUTION :
Let the radius of first circle be r1cm and the radius of second circle be r2 cm.
Given :
r1 + r2 = 140cm ………... (1)
2πr1 – 2πr2 = 88cm
2π(r1 - r2) = 88
r1 - r2 = 88/2π
r1 - r2 = 88 × 7/(2 × 22)
r1 - r2 = 2 × 7 = 14 cm
r1 - r2 = 14cm ……... (2)
On adding equation 1 & 2
r1 + r2 = 140
r1 - r2 = 14
-------------------
2r1 = 154
r1 = 154/2
r1 = 77cm
On putting the value of r1 in equation 1,
r1 + r2 = 140
77 + r2 = 140 cm
r2 = 140 – 77 = 63
r2 = 63 cm
Diameter of first circle = 2 × Radius = 2 × r1 = 2×77 = 154cm
Diameter of first circle = 154 cm
Diameter of second circle = 2 × r2 = 2 × 63 = 126 cm
Diameter of second circle = 126 cm
Hence, diameter of the circles are 154 cm & 126 cm.
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Answer:
Required diameters of the two
circles are D =154 cm
d = 126cm
Explanation:
Let R,r are radii of two circles.
Sum of the radii = 140cm[given]
=> R+r = 140
Multiply each term by 2 , we get
=> 2R+2r = 280
=> D + d = 280 ----(1)
[ Here , D = 2R, d = 2r
diameters of two circles ]
and
Difference of the circumstances = 88cm[given]
=> πD - πd = 88
=> π(D-d) = 88
=> D-d = 88/π
=> D-d = 88 × (7/22)
=> D-d = 28 ---(2)
Add equations (1) & (2), we get
=> 2D = 308
=> D = 154cm
Put D = 154cm in equation (1),
we get
154 + d = 280
=> d = 280 -154
=> d = 126 cm
Therefore,
Required diameters of the two
circles are D =154 cm
d = 126cm
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