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Question

Statement 1: The area of a quarter circle is one-fourth of that of a circle with the same radius.

Statement 2: The circumference of a quarter circle is one-fourth of that of a circle with the same radius.


A

Both the statements are true

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B

Statement 1 is true and statement 2 is false

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C

Statement 1 is false and statement 2 is true

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D

Both the statements are false

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Solution

The correct option is B

Statement 1 is true and statement 2 is false


The area of a quarter circle is one-fourth of that of the complete circle because the area is the region enclosed. For a semi-circle, it is half of the total area and for quarter circle, it is one-fourth. So, area of a quarter circle with radius r=πr24

The circumference is the length of the boundary. For a quarter circle with radius r, circumference is given by (πr2)+2r.

So, statement 1 is true and statement 2 is false.


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