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

1. $2units$
2. $punits$
3. $4units$
4. $7units$

Q. The radii of the two circles are $19\text{cm}$ and $9\text{cm}$ respectively. Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles.

Q. Fig. depicts an archery target marked with its five scoring regions from the centre outwards as Gold, Red, Blue, Black and White. The diameter of the region representing gold score is $21cm$ and each of the other bands is $10.5cm$ wide. Find the area of each of the five scoring regions

Q. The radii of two circles are $8cm$ and $6cm$ respectively. Find the radius of the circle having area equal to the sum of the areas of the two circles

Q.

Each wheel of a car is of diameter $80cm$. How many complete revolutions does each wheel make in $10$ minutes when the car is travelling at a speed of $66kmper$ hour?

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

Q.

A horse is tied to a peg at one corner of a square shaped grass field of side $15m$ by means of a $5m$ long rope. Find
(i) the area of that part of the field in which the horse can graze.
(ii) The increase in the grazing area if the rope were $10m$ long instead of $5m$. (Use $\pi =3.14$)

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

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. A chord of a circle of radius $10cm$ subtends a right angle at the centre. Find the area of the corresponding (i) Minor segment, (ii) Major segment. (use $\pi =3.14$)

Q. A chord of radius $12cm$ subtends an angle of ${120}^{\circ }$ at the centre. Find the area of corresponding segment of the circle. $(22/7=3.14$ and root $3=1.73)$.

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

Q. A brooch is made with silver wire in the form of a circle with diameter $35mm$. The wire is also used in making $5$ diameters which divide the circle into $10$ equal sectors as shown in fig find:
(i) The total length of the silver wire required.
(ii) The arc of each sector of the brooch

Q. In a circle of radius $21cm$, an arc subtends and angle of ${60}^{\circ }$ at the centre. Find:
(i) The length of the arc (ii) Area of the sector formed by the arc (iii) Area of the segment formed by the corresponding chord

Q. An umbrella has $8$ ribs which are equally spaced . Assuming umbrella to be a flat circle of radius $45$ cm, find the area between the two consecutive ribs of the umbrella.

Q. Find the area of the shaded region in figure, if radii of the two concentric circles with center $O$ are 7 cm and 14 cm respectively and $\angle AOC={40}^{\circ }$.

Q. Find the area of the shaded region in fig., if $PQ=24cm,PR=7cm$ and $O$ is the centre of the circle.

Q. Find the area of the shaded region in Fig., if ABCD is a square of side $14cm$ and $APD$ and $BPC$ are semicircles.

Q. From each corner of a square of side $4cm$ a quadrant of a circle of radius $1cm$ is cut and also a circle of diameter $2cm$ is cut as shown in fig. Find the area of the remaining portion of the square.

Q. Find the area of the shaded region in fig, where is circular arc of radius $6cm$ has been drawn with vertex $O$ of an equilateral triangle $OAB$ of side $12cm$ as centre