Question

7. The sum of the radi of two circles is 7 cm, and the difference of their
circumferences is 8 cm. Find the circumferences of the circles.
hon outor and inner radii are respectively​

Answer 1

Question:

The sum of radii of two circles is 7 cm and the difference of their circumferences is 8 cm. Find the circumferences of the circle.

Answer:

Circumference of first circle = 26 m

Circumference of second circle = 18 m

Step-by-step explanation:

Given:

• Sum of radii of the circles = 7 cm
• Difference of the circumference = 8 cm

To Find:

• The circumferences of the circles

Solution:

Let R be the radius of the first circle.

Let r be the radius of the second circle.

By given,

Sum of radii = 7 cm

R + r = 7

r = 7 - R ------(1)

Now,

Circumference of a circle = 2 π r

where r is the radius of the circle.

Hence,

Circumference of first circle = 2 π R

Circumference of second circle = 2 π r

By given,

Difference between the circumferences = 8 cm

Hence,

2 π R - 2 π r = 8

Taking 2 π as common,

2π (R - r) = 8

Substitute the value of r from equation 1

2 π (R - (7 - R))= 8

2 π ( R - 7 + R) = 8

π (2R - 7) = 4

2R - 7 = 1.27

2R = 8.27

R = 4.135 m

Hence radius of the first circle = 4.135 m

Circumference of the first circle = 2 π r = 2 × 3.14 × 4.135

Circumference of first circle = 26 m

Substitute the value of R in equation 1

r = 7 - 4.135

r = 2.865 m

Hence radius of the second circle = 2.865 m

Circumference of second circle = 2 π r = 2 × 3.14 × 2.865

Circumference of second circle = 18 m

Verification:

Sum of radii = 7

2.865 + 4.135 = 7

7 = 7

Difference of circumferences = 8

26 - 18 = 8

8 = 8

Hence verified.