Area of a Circle

Q.

Find the area of a circle with radius $7cm$.

Q. The ratio of radii of two circles is 4 : 5, what is the ratio of their circumference ?

1. 3 : 2
2. 2 : 3
3. 4 : 5
4. 5 : 4

Q. In ☐ ABCD, l(AB) = 13 cm, l(DC) = 9 cm, l(AD) = 8 cm, find the area of ☐ ABCD.

Q. Area of the full circle is $\frac{1}{2}\pi r^2$ where $r$ is the radius of the circle.

1. True
2. False

Q.

Find the area of the following circles, given that: Radius $=14mm.$

Q.

If the radius of a circle is increased to twice its original length, how much will the area of the circle increase?

1. $1.4$ times

2. $2$ times

3. $3$ times

4. $4$ times

Q. In the above figure, if shaded portion has been cut-out from a circle A of diameter 112 cm and centre O. Then, the area of the remaining part of the circle is equal to ___

1. 3 times area of shaded figure
2. 2 times area of shaded figure
3. area of shaded figure
4. none of these

Q. Match the following parts of the circle with their respective areas.

1. $\pi r^2$
2. $\frac{1}{4}\pi r^2$
3. $\frac{1}{2}\pi r^2$

Q. The area of the circle with diameter 10 ft is sq. ft. (round off to 2 decimal places)
$\text{[Take 𝛑=}\frac{22}{7}]$

1. 31.4
2. 78.57
3. 39.28
4. 15.7

Q. What is the appoximate area of a circle whose diameter measures $14$ units? $(\text{take}\pi =\frac{22}{7})$

1. $150uni{t}^2$
2. $152uni{t}^2$
3. $154uni{t}^2$
4. $156uni{t}^2$

Q. If the area of a circle is 154 sq. cm, then find its diameter.

1. 7 cm
2. 56 cm
3. 28 cm
4. 14 cm

Q.

The circumference of circle K is $\pi$. The circumference of Circle L is $4\pi$. What is the value of the ratio of their circumferences? Of their radii? Of their areas?

Q. The area of the segment in a quarter of a circle of radius 8 inches is
$inche{s}^2$

1. $16\pi +32$
2. $16\pi -8$
3. $16\pi -32$

Q. The length of a minute hand of a wall clock is $8.4cm$. Find the area swept by it in half an hour.

1. $100c{m}^2$
2. $120c{m}^2$
3. $110.88c{m}^2$
4. $130c{m}^2$

Q. In a city, there are 1200 lamp posts. The radius of each lamp post is 7cm and height is 12m.find the total cost of painting the curved surface area of all the lamp posts at the rate of ₹24 per m

Q. If the area of a circle is 44 sq. m, what is the area of its quadrant?

Q. If the radii of two wheels are in the ratio $3:7,$ then the ratio of their areas is:

1. $9:49$
2. $49:9$
3. $6:14$
4. $3:49$

Q. Find the area of a circle whose circumference is the sum of the circumferences of two circles with radii 8 and 6 units..

1. 
   $626c{m}^2$
2. 
   $636c{m}^2$
3. 
   $616c{m}^2$
4. 
   $606c{m}^2$

Q. The area of the circular ring included between two concentric circles of radii 3 cm and 2 cm is:

1. $\pi {\text{cm}}^2$
2. $13\pi {\text{cm}}^2$
3. $10\pi {\text{cm}}^2$
4. $5\pi {\text{cm}}^2$

Q. Find the area of a circle whose circumference is $220$ m.

Q. If the area of a circle is 88 sq. m, what is the area of its quadrant?

1. 66 sq. m
2. 22 sq. m
3. 44 sq. m
4. 55 sq. m

Q. The diameters of two circles are $32cm$ and $24cm$ . Find the radius of the circle having its area equal to sum of the areas of the two given circle.

1. $20cm$
2. $41cm$
3. $62cm$
4. $52cm$

Q. Given the area $a$ of a circle is $154uni{t}^2$, what is its radius $r$?

1. $r=5units$
2. $r=6units$
3. $r=7units$
4. $r=8units$

Q. The area of a circle is A. Find the new area of the circle if its radius is reduced to half.

1. 0.5A
2. 0.75A
3. A
4. 0.25A

Q. A circle is inscribed in a square and then a smaller square is inscribed in the circle. The ratio of the area of the smaller square to that of the larger square is

1. $1:4$
2. $\sqrt{2}:2$
3. $1:2$
4. $1:\sqrt{2}$
5. $2:3$

Q. The area of a circle is approximated to be $314uni{t}^2$. What is the measure of its diameter? (take $\pi =3.14$)

1. $10$ $units$
2. $15$ $units$
3. $20$ $units$
4. $25$ $units$

Q. The given figure shows the center of a circular arc and AOB is a straight line. Find the perimeter and the area of the shaded region correct to one decimal place. (Take $\pi =3.142$)

Q. In the given figure, diameter of the small circle is $36cm$ and diameter of the largest semicircle is $107cm$. Find the area of the shaded region.

Q. Given a circle of radius $r=7units$, the area of the circle is . $(\text{take}\pi =\frac{22}{7})$

1. $150uni{t}^2$
2. $154uni{t}^2$
3. $158uni{t}^2$
4. $162uni{t}^2$

Q. Given that the area $a$ of a circle with radius $r$ and diameter $d$ is $100uni{t}^2$, what is the value of $d^2$?

1. $\frac{200}{\pi }$
2. $\frac{300}{\pi }$
3. $\frac{400}{\pi }$
4. $\frac{500}{\pi }$