Question 1

If the circumference of a circle is 44 cm, then its area is:

Accepted Answer

The circumference of the circle is given as $2\pi r = 44$. Therefore, $2 	imes \frac{22}{7} 	imes r = 44$, which gives $r = 7$ cm. The area of the circle is $\pi r^2 = \frac{22}{7} 	imes 7 	imes 7 = 154	ext{ cm}^2$.

Question 2

Area of a circle of radius $r$ is given by:

Accepted Answer

The standard formula for the area of a circle with radius $r$ is $\pi r^2$.

Question 3

The area of a quadrant of a circle whose circumference is 22 cm is:

Accepted Answer

Given circumference $2\pi r = 22$, so $r = \frac{22}{2\pi} = \frac{11}{\pi}$. Area of the quadrant = $\frac{1}{4} \pi r^2 = \frac{1}{4} 	imes \pi 	imes \left(\frac{11}{\pi}ight)^2 = \frac{1}{4} 	imes \frac{121}{\pi} = \frac{121}{4 	imes \frac{22}{7}} = \frac{121 	imes 7}{4 	imes 22} = \frac{

Question 4

If the radius of a circle is doubled, its area becomes:

Accepted Answer

Original area $A1 = \pi r^2$. New radius $= 2r$. New area $A2 = \pi (2r)^2 = 4\pi r^2 = 4 A1$. Thus, the area becomes 4 times.

Question 5

The length of an arc of a sector of angle $	heta$ in a circle of radius $r$ is:

Accepted Answer

The formula for the length of an arc of a sector subtending an angle $	heta$ at the centre is $\frac{	heta}{360^\circ} 	imes 2\pi r$.

Areas Related to Circles