Question

Math Expert

The sum of the radii of two circles is 140 cm and the difference of their circumferences in 88 cm.​

Answer 1

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.

Answer 2

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 .