Question 12

Given below are two statements:

Statement I : The ratio of the circumference of two circles is 3:4, then the ratio of
their area is 9: 16.

Statement II : If the circumference and the area of a circle are numerical equal, then
the diameter is equal to 4.

In the light of the above statements, choose the correct answer from the options given below.

Solution

Statement I: The ratio of the circumference of two circles is 3:4

So, ratio of their radius = 3:4

Now, ratio of their area will be equal to square of the ratio of their radius = $$3^2:4^2=9:16$$

So, statement I is true.

Statement II: The circumference and the area of a circle are numerically equal

or, $$2\pi\ r=\pi\ r^2$$

or, $$r=2$$ units

So, diameter = $$2r=2\times\ 2=4$$ units

So, statement II is true.

So, both statement I and statement II are true.

So, correct answer is option A.

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