Areas Related to Circles: 1 mark Questions (CBSE Class 10)

Chord AB subtends an angle of $40^{\circ }$ at the centre of the circle of radius 9 cm. The length of arc AB is :

1. (A)$\frac{22}{7}$ cm
2. (B)$\frac{198}{7}$ cm
3. (C)$\frac{44}{7}$ cm
4. (D)$\frac{54}{7}$ cm

An arc of length 11 cm subtends an angle of $105^{\circ }$ at the centre of the circle. The radius of the circle is :

1. (A)8 cm
2. (B)$4\sqrt{3}$ cm
3. (C)6 cm
4. (D)7 cm

The length of a pendulum is 70 cm and it describes an arc of length 88 cm when swings. The angle subtended by the arc at the centre is

1. (A)$36^{\circ }$
2. (B)$70^{\circ }$
3. (C)$72^{\circ }$
4. (D)$80^{\circ }$

The length of the arc of the sector of a circle with radius 21 cm and of central angle $60^{\circ }$, is :

1. (A)22 cm
2. (B)44 cm
3. (C)88 cm
4. (D)11 cm

The hour hand of a clock is 7 cm long. The angle swept by it between 7:00 a.m. and 8:10 a.m. is :

1. (A)${\left(\frac{35}{4}\right)}^{\circ }$
2. (B)${\left(\frac{35}{2}\right)}^{\circ }$
3. (C)$35^{\circ }$
4. (D)$70^{\circ }$

Shown in the given figure is a circle with centre O. The area of the minor sector is 7 cm${}^2$. Area of circle is :

1. (A)$84\pi$ cm${}^2$
2. (B)$\frac{84}{11}$ cm${}^2$
3. (C)84 cm${}^2$
4. (D)$\frac{\sqrt{84}}{\sqrt{\pi }}$ cm${}^2$

In the given figure, O is the centre of circle. XYZ is an arc of the circle subtending an angle of $45^{\circ }$ at the centre. If the radius of the circle is 32 cm, then the length of the arc XYZ is :

1. (A)$4\pi$ cm
2. (B)$8\pi$ cm
3. (C)$64\pi$ cm
4. (D)$128\pi$ cm

Area of a segment of a circle of radius 'r' and central angle $60^{\circ }$ is :

1. (A)$\frac{\pi r^2}{2}-\frac{1}{2}{r}^2$
2. (B)$\frac{2\pi r}{4}-\frac{\sqrt{3}}{4}{r}^2$
3. (C)$\frac{\pi r^2}{6}-\frac{\sqrt{3}}{4}{r}^2$
4. (D)$\frac{2\pi r}{4}-r^2\sin 60^{\circ }$

The area of a semicircle of diameter 'd' is :

1. (A)$\frac{\pi d^2}{16}$
2. (B)$\frac{\pi d^2}{4}$
3. (C)$\frac{\pi d^2}{8}$
4. (D)$\frac{\pi d^2}{2}$

A circle is divided into 16 identical sectors. If radius of the circle is 7 cm, area of each sector is

1. (A)$\frac{77}{4}$ cm${}^2$
2. (B)77 cm${}^2$
3. (C)154 cm${}^2$
4. (D)$\frac{77}{8}$ cm${}^2$

Arc PQ subtends an angle $\theta$ at the centre of the circle with radius 6.3 cm. If $\stackrel{⌢}{\mathrm{PQ}}=11$ cm, then the value of $\theta$ is

1. (A)$10^{\circ }$
2. (B)$60^{\circ }$
3. (C)$45^{\circ }$
4. (D)$100^{\circ }$

Area of sector of a circle with radius 18 cm is 198 cm${}^2$. The measure of central angle is

1. (A)$70^{\circ }$
2. (B)$14^{\circ }$
3. (C)$140^{\circ }$
4. (D)$210^{\circ }$

An arc of length 2.2 cm subtends an angle $\theta$ at the centre of the circle with radius 2.8 cm. The value of $\theta$ is

1. (A)$50^{\circ }$
2. (B)$60^{\circ }$
3. (C)$45^{\circ }$
4. (D)$30^{\circ }$

The area of a sector of a circle of radius 10 cm is $\frac{55}{3}$ $c{m}^2$. The value of central angle is

1. (A)$\frac{21^{\circ }}{2}$
2. (B)$42^{\circ }$
3. (C)$105^{\circ }$
4. (D)$21^{\circ }$

The perimeter of the shaded region in the given figure is :

1. (A)$l$
2. (B)$l+a$
3. (C)$l+2r$
4. (D)$l+2r+a$

The ratio of the area of a quadrant of a circle to the area of the same circle is :

1. (A)1 : 2
2. (B)2 : 1
3. (C)1 : 4
4. (D)4 : 1

In the given figure, the shaded region represents :

1. (A)minor sector
2. (B)major sector
3. (C)minor segment
4. (D)major segment

The perimeter of a quadrant of a circle of radius r is :

1. (A)$\frac{1}{4}\pi r^2$
2. (B)$\frac{1}{4}\pi r^2+2r$
3. (C)$\frac{\pi r}{2}$
4. (D)$\frac{\pi r}{2}+2r$

The area of a quadrant of a circle of radius ‘2r’ is :

1. (A)$\frac{1}{4}\pi r^2$
2. (B)$\frac{1}{2}\pi r^2$
3. (C)$\pi r^2$
4. (D)$2\pi r^2$

The ratio of the area of a quadrant of a circle to the area of a circle is :

1. (A)2 : 1
2. (B)1 : 2
3. (C)1 : 4
4. (D)4 : 1

The angle of the sector of a circle whose area is one-eighth of the area of the circle is :

1. (A)$22{\frac{1}{2}}^{\circ }$
2. (B)$45^{\circ }$
3. (C)$60^{\circ }$
4. (D)$90^{\circ }$

The perimeter of a quadrant of a circle of circumference 22 cm is :

1. (A)29 cm
2. (B)22 cm
3. (C)12.5 cm
4. (D)5.5 cm

The length of arc subtending an angle of $210^{\circ }$ at the centre of the circle, is $\frac{44}{3}$ cm. The radius of the circle is :

1. (A)$2\sqrt{2}$ cm
2. (B)4 cm
3. (C)8 cm
4. (D)$\frac{1}{4}$ cm

The perimeter of a quadrant of a circle of radius 7 cm, is :

1. (A)18 cm
2. (B)11 cm
3. (C)22 cm
4. (D)25 cm

An arc of length 22 cm subtends an angle of $x^{\circ }$ at the centre of the circle. If radius of circle is 36 cm, the value of $x$ is

1. (A)35
2. (B)40
3. (C)60
4. (D)30

An arc of length '$l$' subtends an angle of $15^{\circ }$ at the centre of a circle of radius 8.4 cm. The value of $l$ is

1. (A)22 cm
2. (B)2.2 cm
3. (C)9.24 cm
4. (D)4.2 cm

OAB is sector of a circle with centre O and radius 7 cm. If length of arc $\stackrel{⌢}{\mathrm{AB}}=\frac{22}{3}$ cm, then $\angle AOB$ is equal to

1. (A)${\left(\frac{120}{7}\right)}^{\circ }$
2. (B)$45^{\circ }$
3. (C)$60^{\circ }$
4. (D)$30^{\circ }$

If a sector of a circle has an area of $40\pi$ sq. units and a central angle of $72^{\circ }$, the radius of the circle is :

1. (A)$200$ units
2. (B)$100$ units
3. (C)$20$ units
4. (D)$10\sqrt{2}$ units

A piece of wire $20$ cm long is bent into the form of an arc of a circle of radius $\frac{60}{\pi }$ cm. The angle subtended by the arc at the centre of the circle is :

1. (A)$30^{\circ }$
2. (B)$60^{\circ }$
3. (C)$90^{\circ }$
4. (D)$50^{\circ }$

An arc of a circle is of length $5\pi$ cm and the sector it bounds has an area of $20\pi$ cm${}^2$. Its radius is :

1. (A)$10$ cm
2. (B)$1$ cm
3. (C)$5$ cm
4. (D)$8$ cm

If a large circular pizza is divided into 5 equal sectors, then the central angle of each sector will be :

1. (A)$60^{\circ }$
2. (B)$90^{\circ }$
3. (C)$45^{\circ }$
4. (D)$72^{\circ }$

If an arc of a circle of diameter 10 cm subtends an angle of $144^{\circ }$ at the centre of the circle, then the length of the arc is :

1. (A)$2\pi$ cm
2. (B)$4\pi$ cm
3. (C)$5\pi$ cm
4. (D)$6\pi$ cm

If the area of a sector of circle of radius 36 cm is $54\pi$ cm${}^2$, then the length of the corresponding arc of the sector is :

1. (A)$8\pi$ cm
2. (B)$6\pi$ cm
3. (C)$4\pi$ cm
4. (D)$3\pi$ cm

The diameter of a wheel is 63 cm. The distance travelled by the wheel in 100 revolutions is :

1. (A)99 m
2. (B)198 m
3. (C)63 m
4. (D)136 m

The difference of the areas of a minor sector of angle $120^{\circ }$ and its corresponding major sector of a circle of radius 21 cm, is

1. (A)231 cm${}^2$
2. (B)462 cm${}^2$
3. (C)346.5 cm${}^2$
4. (D)693 cm${}^2$

In the given figure, two concentric circles of radii 5 cm and 3 cm have their centre O. OAB is a sector of outer circle making an angle of $60^{\circ }$ at the centre while OCD is the sector of smaller circle. The area of the shaded region is :

1. (A)$\frac{7\pi }{2}$ cm${}^2$
2. (B)$\frac{8\pi }{3}$ cm${}^2$
3. (C)$\frac{25\pi }{6}$ cm${}^2$
4. (D)$\frac{3\pi }{2}$ cm${}^2$

The region between a chord and either of the two arcs of a circle is called :

1. (A)an arc
2. (B)a sector
3. (C)a segment
4. (D)a semicircle

In a circle of radius 21 cm, if an arc subtends an angle of $60^{\circ }$ at the centre of the circle, then the length of the arc is :

1. (A)11 cm
2. (B)44 cm
3. (C)$\frac{22}{7}$ cm
4. (D)22 cm

Area of a sector of angle $\theta$ (in degrees) of a circle with radius $r$ is :

1. (A)$\frac{\theta }{180}\times 2\pi r$
2. (B)$\frac{\theta }{180}\times \pi r^2$
3. (C)$\frac{\theta }{360}\times 2\pi r$
4. (D)$\frac{\theta }{720}\times 2\pi r^2$

The area of the sector of a circle with radius 6 cm which subtends an angle of $60^{\circ }$ at the centre of the circle is :

1. (A)$\frac{142}{7}$ cm${}^2$
2. (B)$\frac{152}{7}$ cm${}^2$
3. (C)$\frac{132}{7}$ cm${}^2$
4. (D)$\frac{122}{7}$ cm${}^2$

If the area of a sector of a circle is $\frac{1}{8}$ of the area of the circle, then the central angle of the sector is :

1. (A)$30^{\circ }$
2. (B)$45^{\circ }$
3. (C)$60^{\circ }$
4. (D)$90^{\circ }$

The length of an arc of a circle with radius 12 cm is $10\pi$ cm. The central angle subtended by this arc at the centre, is :

1. (A)$120^{\circ }$
2. (B)$6^{\circ }$
3. (C)$75^{\circ }$
4. (D)$150^{\circ }$

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

1. (A)$\frac{11}{4}$ cm${}^2$
2. (B)$\frac{11}{2}$ cm${}^2$
3. (C)$\frac{33}{4}$ cm${}^2$
4. (D)$\frac{77}{8}$ cm${}^2$

The area of a sector of a circle of radius 16 cm cut off by an arc, which is 18.5 cm long, is :

1. (A)168 cm${}^2$
2. (B)148 cm${}^2$
3. (C)154 cm${}^2$
4. (D)176 cm${}^2$

Perimeter of a sector of a circle whose central angle is $90^{\circ }$ and radius 7 cm is :

1. (A)35 cm
2. (B)11 cm
3. (C)22 cm
4. (D)25 cm

If the area of a sector of a circle is $\frac{7}{20}$ of the area of the circle, then the angle at the centre is equal to

1. (A)$110^{\circ }$
2. (B)$130^{\circ }$
3. (C)$100^{\circ }$
4. (D)$126^{\circ }$

If an arc subtends an angle of $90^{\circ }$ at the centre of a circle, then the ratio of its length to the circumference of the circle is :

1. (A)2 : 3
2. (B)1 : 4
3. (C)4 : 1
4. (D)1 : 3

The area of the sector of a circle of radius 12 cm is $60\pi$ cm${}^2$. The central angle of this sector is :

1. (A)$120^{\circ }$
2. (B)$6^{\circ }$
3. (C)$75^{\circ }$
4. (D)$150^{\circ }$

Assertion (A) : If the circumference of a circle is 176 cm, then its radius is 28 cm.
Reason (R): Circumference = $2\pi \times$ radius of a circle.

1. (A)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
2. (B)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
3. (C)Assertion (A) is true, but Reason (R) is false.
4. (D)Assertion (A) is false, but Reason (R) is true.

If in the given figure, $\angle C=\angle D=90^{\circ }$, $\angle B=60^{\circ }$ and AP = 3 cm, then the area of the shaded region is :

1. (A)$3\pi$ cm${}^2$
2. (B)$6\pi$ cm${}^2$
3. (C)$7\pi$ cm${}^2$
4. (D)$9\pi$ cm${}^2$

The area of the square inscribed in a circle of radius $5\sqrt{2}$ cm is :

1. (A)50 cm${}^2$
2. (B)100 cm${}^2$
3. (C)25 cm${}^2$
4. (D)200 cm${}^2$

The perimeter of the sector of a circle of radius 21 cm which subtends an angle of $60^{\circ }$ at the centre of circle, is :

1. (A)22 cm
2. (B)43 cm
3. (C)64 cm
4. (D)462 cm

The length of an arc of a circle with radius 12 cm is $10\pi$ cm. The angle subtended by the arc at the centre of the circle, is :

1. (A)$120^{\circ }$
2. (B)$6^{\circ }$
3. (C)$75^{\circ }$
4. (D)$150^{\circ }$

The area of a sector of angle $\alpha$ (in degrees) of a circle with radius R is :

1. (A)$\frac{\alpha }{180}\times 2\pi R$
2. (B)$\frac{\alpha }{360}\times 2\pi R$
3. (C)$\frac{\alpha }{180}\times \pi R^2$
4. (D)$\frac{\alpha }{360}\times \pi R^2$

If the radius of a semi-circular protractor is 7cm, then its perimeter is :

1. (A)11 cm
2. (B)14 cm
3. (C)22 cm
4. (D)36 cm

The length of the arc of a circle of radius 14 cm which subtends an angle of $60^{\circ }$ at the centre of the circle is :

1. (A)$\frac{44}{3}$ cm
2. (B)$\frac{88}{3}$ cm
3. (C)$\frac{308}{3}$ cm
4. (D)$\frac{616}{3}$ cm

If the perimeter and the area of a circle are numerically equal, then the radius of the circle is :

1. (A)2 units
2. (B)$\pi$ units
3. (C)4 units
4. (D)$2\pi$ units

What is the length of arc of a circle of radius 7 cm which subtends an angle of $90^{\circ }$ at the centre of the circle ?

1. (A)22 cm
2. (B)11 cm
3. (C)$\frac{77}{2}$ cm
4. (D)$\frac{11}{2}$ cm

Area of a quadrant of a circle of radius 7 cm is

1. (A)154 cm${}^2$
2. (B)77 cm${}^2$
3. (C)$\frac{77}{2}$ cm${}^2$
4. (D)$\frac{77}{4}$ cm${}^2$

What is the length of the arc of the sector of a circle with radius 14 cm and of central angle $90^{\circ }$ ?

1. (A)22 cm
2. (B)44 cm
3. (C)88 cm
4. (D)11 cm

The hour-hand of a clock is 6 cm long. The angle swept by it between 7:20 a.m. and 7:55 a.m. is :

1. (A)${\left(\frac{35}{4}\right)}^{\circ }$
2. (B)${\left(\frac{35}{2}\right)}^{\circ }$
3. (C)$35^{\circ }$
4. (D)$70^{\circ }$

What is the area of a semi-circle of diameter ‘d’ ?

1. (A)$\frac{1}{16}\pi d^2$
2. (B)$\frac{1}{4}\pi d^2$
3. (C)$\frac{1}{8}\pi d^2$
4. (D)$\frac{1}{2}\pi d^2$

The circumferences of two circles are in the ratio 4 : 5. What is the ratio of their radii ?

1. (A)16 : 25
2. (B)25 : 16
3. (C)$2:\sqrt{5}$
4. (D)4 : 5