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If the radius of the circle is increased by $1 cm,$ then what is the ratio of the new circumference to its new diameter?

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π : 1

2 : 1

None of these

π : 2

answer is A.

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Detailed Solution

Given that, the radius of a circle is increased by 1 cm.
Diameter of a circle is twice its radius.
Circumference of a circle of radius r is equal to

2 π r

.
Let

r

be the radius of the circle initially.
Add 1 to r to find the new radius.

R = r + 1

Multiply

R

by 2 to determine the new diameter.

D

= 2

× R

\Rightarrow

2 (r + 1) ...........(1)
Multiply R by

2 π

to determine the new circumference.
C = 2

π × R

\Rightarrow C

= 2

π

(r + 1) ................(2)
Divide equation (2) by equation (1) to determine the ratio of new circumference of the circle to its new diameter.

C D = 2 π × R

⇒ 2 π (r + 1+) 2 (r + 1 )

\Rightarrow

π 1

Therefore, the radius of a circle is increased by 1 cm, then the ratio of new circumference of the circle to its new diameter is

π

: 1 .
Hence the correct option is 1.

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