Question

8. 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​

Answer 1

GIVEN :

Sum of radii of two circles = 140cm

Let the two radii be = R and r

R + r = 140 -----(1)

Difference between circumferences = 88

We know that,

Circumference = 2πr

2πR - 2πr = 88

2π(R - r) = 88

R - r = 88 ÷ 44/7

R - r = 88 × 7/44

R - r = 2 × 7

R - r = 14 -----(2)

Now solve the eq - (1) & 2

R + R + r - r = 140 + 14

2R = 154

R = 154/2

R = 77

Substitute R in eq - (1)

R + r = 140

77 + r = 140

r = 140 - 77

R = 63

The radii of two circles = 77cm and 63cm

Then,

Diameter = ?

We know that,

Diameter = 2 × radius

= 2 × 77

= 154cm

= 2 × 63

= 126cm

Therefore, the diameters of two circles are 154cm and 126cm.

Answer 2

Answer:

Diameter of circle (i)=2r1= 2 x 77 = 154cm

Diameter of circle (i)=2r2= 2 x 63 = 126cm

Step-by-step explanation:

Given problem:

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​.

Solution:

To Find:

Let radius of circles be r1 and r2

Given that,

Sum of the radius = 140cm.

It means,

We have,

r1+r2=140 .......Equation(i)

Now,

Difference in circumferences= 88

2πr1-2πr2= 88

We know that,

Circumference = 2πr

$\implies\ 2 \times\dfrac{22}{7} (r_1 - r_2) \: 88$

$\implies r_1 - r_2 = \dfrac{88\times7}{2\times\ 22} = 14$

$\implies\ r_1 = r_2 + 14 ..........(Eqn)2$

$\implies\ Now, eq 1 \:in\:2 \implies\ r_2 + r_2 + 14 = 140$

$\implies\ 2r_2 = 126$

$\implies\ r_2 = \dfrac{126}{2} = 63 cms$

$\implies\ r_2 = 63 cm\: in (ii) r_1=63+14=77cm$

We know that,  

Diameter = 2 × radius.

So,

Diameter of circle (i) = 2r1 = 2 x 77 = 154cm.

Diameter of circle (ii)= 2r2= 2 x 63 = 126cm.

Therefore,

The diameters of two circles are 154cm and 126cm.