Areas of Sector and Segment of a Circle

If the area of the shaded region in the given figure is $k {\mathrm{cm}}^2$ and if $\mathrm{P}\mathrm{Q}=24 \mathrm{c}\mathrm{m}, \mathrm{P}\mathrm{R}=7 \mathrm{c}\mathrm{m}$ and $\mathrm{O}$ is the centre of the circle. Find $k$. [write the answer up to two decimal places and use $\mathrm{\pi }=\frac{22}{7}$].
   

A brooch is made with silver wire in the form of a circle with diameter $35 \mathrm{m}\mathrm{m}.$ The wire is also used in making $5$ diameters which divide the circle into $10$equal sectors as shown in the below figure. Find the area of each sector of the brooch.

A horse is tied to a peg at one corner of a square shaped grass field of side $15 \mathrm{m}$ by means of a $5 \mathrm{m}$ long as given in figure. Find the increase in the grazing area if the rope were $10 \mathrm{m}$ long instead of $5\mathrm{}\mathrm{m}.$ (use $\pi =\mathrm{}3.14$)

In a circle of radius $21 \mathrm{c}\mathrm{m},$ an arc subtends an angle of ${60}^{\mathrm{o}}$ at the centre.

Find the area of the segment formed by the corresponding chord

In a circle of radius $21 \mathrm{c}\mathrm{m},$ an arc subtends an angle of ${60}^{\mathrm{o}}$ at the centre.
Find area of the sector formed by the arc

A chord of a circle of radius $10 \mathrm{c}\mathrm{m}$ subtends a right angle at the centre. Find the area of the corresponding major sector.
(Use $\pi =3.14)$

Area of a sector of angle $p$ in degrees of a circle with radius $R$ is

A round table cover has six equal designs as shown in figure. If the radius of the cover is $28 \mathrm{c}\mathrm{m},$find the cost of making the designs at the rate of $\mathrm{R}\mathrm{s}.0.35$ per ${\mathrm{c}\mathrm{m}}^2.$ (Use $\sqrt{3}=1.7$)

To warn ships for underwater rocks, a lighthouse spreads a red coloured light over a sector of angle $80°$ to a distance of $16.5 \mathrm{km}$. Find the area of the sea over which the ships warned (Use $\pi =3.14$).

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

An umbrella has $8$ ribs which are equally spaced as shown in figure. Assuming umbrella to be a flat circle of radius $45 \mathrm{c}\mathrm{m},$ find the area between the two consecutive ribs of the umbrella.

A brooch is made with silver wire in the form of a circle with diameter $35 \mathrm{m}\mathrm{m}.$ The wire is also used in making$5$diameters which divide the circle into $10$equal sectors as shown in figure. Find the total length of the silver wire required.

A horse is tied to a peg at one corner of a square shaped grass field of side $15 \mathrm{m}$ by means of a $5 \mathrm{m}$ long rope (see Fig.$12.11)$. Find the area of that part of the field in which the horse can graze.
(use $\pi =\mathrm{}3.14$)
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A chord of a circle of radius $12 \mathrm{c}\mathrm{m}$ subtends an angle of ${120}^{\mathrm{o}}$ at the centre. Find the areas of the corresponding segment of the circle. ( Use $\pi =3.14$ and $\sqrt{3}=1.73$ )

A chord of a circle of radius $15 \mathrm{c}\mathrm{m}$ subtends an angle of $60°$ at the centre. Find the areas of the corresponding minor and major segments of the circle.
(Use $\mathrm{\pi }=3.14$ and $\sqrt{3}\mathrm{}=\mathrm{}1.73$)

In a circle of radius $21 \mathrm{c}\mathrm{m},$ an arc subtends an angle of ${60}^{\mathrm{o}}$ at the centre. Find the length of the arc?

A chord of a circle of radius $10 \mathrm{c}\mathrm{m}$ subtends a right angle at the centre. Find the area of the corresponding minor segment (use $\pi =3.14)$.

The length of the minute hand of a clock is $14 \mathrm{c}\mathrm{m}.$ Find the area swept by the minute hand in $5$ minutes.

Find the area of a quadrant of circle whose circumference is $22 \mathrm{c}\mathrm{m}.$

Find the area of a sector of a circle with radius $6 \mathrm{c}\mathrm{m}$ if angle of the sector is $60°.$