Question

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

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

• A. Both the statements are true
• B. Statement 1 is true and statement 2 is false
• C. Statement 1 is false and statement 2 is true
• D. Both the statements are false

Answer 1

Answer: (A), (B)

The correct options are
A

Both the statements are true

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 $r=\frac{\pi r^2}{4}$

The circumference is the length of the boundary. For a quarter circle with radius r, circumference is given by $\left(\frac{\pi r}{2}\right)+2r$.

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