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The sum of the radii of two circles is 140 cm and the difference of their circumferences in 88 cm.
Answers
Sum of radii of circular top and bottom = 140 cm [ Given ]
Let the radius of top be r cm
- Radius of bottom = ( 140 - r ) cm
- Circumference of top = 2πr cm
- Circumference of bottom = 2πr ( 140 - r ) cm
- Difference of circumference = [ 2πr - 2π( 140 - r ) cm
By the given conditions,
2πr - 2π ( 140 - r ) = 88 [ Given ]
➪ 2π [ r - 140 + r ] = 88
➪ 2r - 140 = 88/2π
➪ 2r - 140 = 44/22/7
➪ 2r - 140 = 44 ×7/22
➪ 2r - 140 = 2 × 7
➪ 2r - 140 = 14
➪ 2r = 14 + 140
➪ 2r = 154
➪ r = 77
Therefore,
Radius of top = 77 cm
➱ Diameter of top = 2 × 77 = 154 cm
Radius of bottom = 140 - r = 140 - 77 = 63 cm
➪ Diameter of bottom = 2 × 63 = 126 cm.
Step-by-step explanation:
r1 + r2 = 140cm equation1 . 2pi r1 - 2pi r2 =88cm .
2pi ( r1 - r2 ) = 88 .
r1 - r2 = 88 2pi.
r1 - r2 = 88 ×7/(2× 22). r1 - r2 = 2 × 7. r1 - r2 = 14cm equation2 . on adding equation1 and 2 . r1+r2 =140cm and r1 - r2 =14 . 2r1 = 154 . r1= 154/2 . r1 = 77 . on putting the value of r1 in equation1 . 77 + r2 =140cm . r2 = 140 - 77. r2 = 63 . so the diameter of first circle = 2× radius = 2× r1 = 2×77 =154cm . and second circle =2×r2 = 2×63 =126cm .