Area of a Sector of a Circle

Q.

The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.

Q. The hour hand of a clock is 6 cm long. The area swept by it between 11.20 am and 11.55 am is

(a) 2.75 cm²

(b) 5.5 cm²

(c) 11 cm²

(d) 10 cm²

Q.

What is the formula used to find the length of the arc of a sector?

Q. Three semicircles each of diameter 3 cm, a circle of diameter 4.5 cm and a semicircle of radius 4.5 cm are drawn in the given figure. Find the are of the shaded region.

Q. Question 1
Find the area of a sector of a circle with radius 6 cm if angle of the sector is ${60}^{\circ }$.

Q.

A sector of a circle of radius 4 cm contains an angle of ${30}^{\circ }$. Find the area of the sector.

Q.

Find the area and perimeter of a sector with a central angle of ${60}^{\circ }$ in a circle of radius $7cm$.

Q.

The length of the minute hand of a clock is 21 cm. The area swept by the minute hand in 10 minutes is

(a) $231c{m}^2$ (b) $210c{m}^2$ (c) $126c{m}^2$ (d) $252c{m}^2$

Q. Question 2
Find the area of a quadrant of a circle whose circumference is 22 cm.

Q. Find the area of sector of circle of radius 21 cm and central angle 120⁰.

Q.

A car has two wipers which do not overlap. Each wiper has a blade of length $25cm$ sweeping through an angle of ${115}^{\circ }$. Find the total area cleaned at each sweep of the blades.

Q.

In the given figure, three sectors of a circle of radius 7 cm, making angles of ${60}^{\circ },{80}^{\circ }and{40}^{\circ }$ at the centre are shaded. Find the area of the shaded region.

Q.

AB is a chord of a circle with centre O and radius 4 cm. AB is of length 4 cm. Find the area of the sector of the circle formed by chord AB.

Q. In the given figure ABCD is a rectangle of dimensions 21 cm $\times$ 14 cm. A semicircle is drawn with BC as diameter. Find the area and the perimeter of the shaded region in the figure.

Q.

Three equal circles, each of radius $6cm$, touch one another as shown in the figure. Find the area enclosed between them.

[ Take $\pi =3.14and\sqrt{3}$ = 1.732.]

Q. Find the area of a quadrant of a circle whose circumference is 44 cm. [CBSE 2011]

Q.

Figure shows a sector of a circle, centre O, containing an angle $\theta {}^{\circ }$. Prove that:

(i) Perimeter of the shaded region is $r(tan\theta +sec\theta +\frac{\pi \theta }{180}-1)$

(ii) Area of the shaded region is $\frac{r^2}{2}(tan\theta -\frac{\pi \theta }{180})$

Q.

In the given figure, ABC is a quadrant of a circle of radius 14 cm and a semicircle is drawn with BC as diameter. Find the area of the shaded region.

Q. An arc of a circle is of length 5π cm and the sector bounded around it has an area of 20π sq cm. Find the radius of the circle.

Q.

A calf is tied with a rope of length 6 m at the corner of a square grassy lawn of side 20 m. If the length of the rope is increased by 5.5 m, find the increase in area of the grassy lawn in which the calf can graze.

Q.

A horse is placed for grazing inside a rectangular field 70 m by 52 m. It is tethered to one corner by a rope 21 m long. On how much area can it graze ? How much area is left ungrazed ?

Q.

A sector is cut from a circle of radius 21 cm. The angle of the sector is ${150}^{\circ }$. Find the length of the arc and the area of the sector.

Q.

The minute hand of a clock is $\sqrt{21}$ cm long. Find the area described by the minute hand on the face of the clock between 7.00 AM and 7.05 AM.

Q.

Calculate the area of the designed region in the given figure common between the two quadrants of the circles of radius 8 cm each.

1. 

2. 

3. 

Q.

In the given figure, OACB is a quadrant of circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the

(i) Quadrant OACB

(ii) Shaded region

Q. Question 3
Find the area of a sector of a circle of radius 28 cm and central angle ${45}^{\circ }$.

Q.

Find the area of a shaded region in the Fig. where a circular arc of radius 7 cm has been drawn with vertex A of an equilateral triangle ABC of side 14 cm as centre. (Use $pi=\frac{22}{7}$ and $\sqrt{3}=1.73$)

Q.

The perimeter of a sector of a circle of radius 5.7 m is 27.2 m. Find the area of the sector.

Q.

A circular disc of radius 6 cm is divided into three sectors with central angles ${90}^{\circ },{120}^{\circ }and{150}^{\circ }$. What part of the whole circle is the sector with central angle ${150}^{\circ }$? Also, calculate the ratio of the areas of the three sectors.

Q.

Sides of a triangular field are 15 m, 16 m and 17 m. With the three corners of the field a cow, a buffalo and a horse are tied separately with ropes of length 7 m each to graze in the field. Find the area of the field which cannot be grazed by three animals.