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
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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
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Verified answer
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:
To Find:
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.