6. The circumference of a circle exceeds its diameter by 30 cm. Find the radius of the cir 7. The ratio of the radii of two circles is 5 : 3. Find the ratio of their circumferences.
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6)
Given :-
The circumference of circle exceeds its diameter by 30 cm
To Find :-
Radius of circle
Solution :-
We know that
Circumference of circle = πd
Let
Diameter of circle = d
Circumference = 30 + d
⇒ 30 + d = π × d
⇒ 30 + d/d = π
⇒ 30/d + d/d = 22/7
⇒ 30/d + 1 = 22/7
⇒ 30/d = 22/7 - 1
⇒ 30/d = 22 - 7/7
⇒ 30/d = 15/7
⇒ 7 × 30 = 15 × d
⇒ 7 × 30/15 = d
⇒ 7 × 2 = d
⇒ 14 = d
Now
Radius = Diameter/2
⇒ Radius = 14/2
⇒ Radius = 7 cm
Therefore, Radius of circle is 7 cm
7)
Given :-
The ratio of the radii of two circles is 5 : 3.
To Find :-
Ratio of their circumference
Solution :-
We know that
Circumference = 2πr
Let the radii of the circles be 5x and 3x
⇒ C/C' = 2 × π × 5x/2 × π × 3x
⇒ C/C' = 5x/3x
⇒ C/C' = 5/3
⇒ C : C' = 5 : 3
Therefore, Ratio of their radii is 5 : 3
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