Question

The sum of circumferences of two circles is 88cm & the difference of their radii is 2cm
Find the radii of the circles.

Answer 1

Step-by-step explanation:

$\bf \huge \: Question \:$

• The sum of circumferences of two circles is 88cm & the difference of their radii is 2cmFind the radii of the circles.

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$\bf \huge \: To \:Find$

• Find the radii of the circles.

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$\bf \huge \: Given \:$

• The sum of circumferences of two circles is 88cm.
• The difference of their radii is 2cm.

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Supposed:-

Radius of first circle$\bf</strong><strong>\: </strong><strong>= r_{</strong><strong>1</strong><strong>}$

Radius of second circle$\bf</strong><strong>\: </strong><strong>= r_{</strong><strong>2</strong><strong>}$

According to the Question:-

The sum of circumferences of two circles is 88cm & the difference of their radius is 2cm.

$\bf</strong><strong>\: </strong><strong>= </strong><strong>2</strong><strong>π</strong><strong>r_{</strong><strong>1</strong><strong>}</strong><strong>+</strong><strong>2πr_{</strong><strong>2</strong><strong>}</strong><strong>=</strong><strong> </strong><strong>8</strong><strong>8</strong><strong>c</strong><strong>m</strong><strong>$

$\bf\: [R_{1}=2+R_{2}]-(1)$

$\bf\: 2π(R_{1}+R_{2})=88cm$

$\bf\: 2π(2+R_{2}+R_{2})=88cm-{using (1)}$

$\bf\: 2π(2+2R_{2})=88cm$

$\bf\: 4π(1+R_{2})=88cm$

$\bf\: 1+R_{2}=88/4π$

$\bf\: 1+R_{2}=7cm\:$

$\bf\red{ R_{2}=6cm}\:$

Since,

$\bf\: R_{1}-R_{2}=2cm\:$

$\bf\: R_{1}-6=2cm \:$

Therefore,

$\bf \red{R_{1}=8cm}$

HENCE,

Radius of first circle$\bf \red{R_{1 }= 8 cm}$

Radius of second circle$\bf \red{R_{2}= 6 cm}$

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Answer 2

GIVEN:

Sum of circumferences of two circles = 88cm

Difference between their radii = 22cm

TO FIND:

Radii of the circles

SOLUTION:

We know that,

Circumference of circle = 2πr

==> 2πR + 2πr = 88

==> R + r = 14 -----(1)

Difference between radii = 2

==> R - r = 2 -----(2)

Solve both eq - (1) & (2)

==> 2R = 16

==> R = 16/2

==> R = 8

One of the Radius = 8cm

Another radius:

==> 8 + r = 14

==> r = 14 - 8

==> r = 6cm

Therefore, the both radii are 8cm and 6cm.