Question 1 :
The length of the minute hand of a clock is 5 cm. Find the area swept by the minute hand during the time period $6\ :\ 05\ am$ and $6\ :\ 40\ am$ .
Question 2 :
A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding major sector.(Use $\pi$=3.14)
Question 3 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bb0273b2305849799f6.png' />
(As shown in the above figure)A horse is tied to a peg at one corner of a square shaped grass field of side 15 m by means of a 5 m long rope . Find the area of that part of the field in which the horse can graze.
Question 4 :
A chord of a circle of radius 20 cm subtends an angle of $90^{\circ}$ at the centre. Find the area of the corresponding major segment of the circle (Use $\pi=3.14$).
Question 5 :
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.
Question 6 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a47273b230584979911.jpeg' />
The above figure depicts an archery target marked with its five scoring regions from centre outwards as gold, red, blue, black and white. The diameter of the region representing gold score is 21 cm and each of the ofher bands is 10.5 cm wide. Find the area of red scoring region.
Question 7 :
The areas of two sectors of two different circles with equal corresponding arc lengths are equal. Is it true or false?
Question 8 :
The radii of two circless are 19 cm and 9 cm, respectively. Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circless.
Question 9 :
Area of a sector of a circle of radius 36 cm is 54 $\pi\ cm^2$ . Find the length of the corresponding arc of the sector.
Question 10 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bbe273b230584979a08.png' />
In the above figure , OACB is a quadrant of a circle with centre O and radius 3.5 cm . If OD = 2 cm , find the area of the quadrant OACB.
Question 11 :
In covering a distance s metres, a circular wheel of radius r metres makes $\frac{s}{2\pi r}$ revolutions. Is it true or false?
Question 12 :
Find the radius of a circle whose circumference is equal to the sum of the circumferences of two circles of radii 15 cm and 18 cm.
Question 13 :
Find the area of a quadrant of a circle whose circumference is 22 cm.
Question 14 :
A cow is tied with a rope of length 14 m at the corner of a rectangular field of dimensions $20m\times16m$. Find the area of the field in which the cow can graze.
Question 15 :
In a circle of radius 21 cm , an arc subtends an angle of $60^{\circ}$ at the centre. Find area of the sector formed by the arc.
Question 16 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bbe273b230584979a07.png' />
In the above figure , nine circular designs each of radius 7 cm are made on a square handkerchief . Find the area of the remaining portion of the handkerchief.
Question 17 :
The area of the square that can be inscribed in a circle of radius 8 cm is
Question 18 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bb5273b2305849799fc.png' />
Find the area of the shaded region in the above figure, if PQ = 24 cm, PR = 7 cm and O is the centre of the circle.
Question 19 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bad273b2305849799f2.png' />
The above image 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 21 cm and each of the other bands is 10.5 cm wide. Find the area of the red scoring region.
Question 20 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bc1273b230584979a0c.png' />
In the above 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.
Question 21 :
If the length of an arc of a circle of radius r is equal to that of an arc of a circle of radius 2r, then the angle of the corresponding sector of the first circle is double the angle of the corresponding sector of the other circle. Is it true or false?
Question 22 :
The area of a square inscribed in a circle of diameter $p\ cm$ is $p^2\ cm^2$. Is it true or false?
Question 23 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bb9273b230584979a01.png' />
(As shown in the above image) In a circular table cover of radius 32 cm , a design is formed leaving an equilateral triangle ABC in the middle . Find the area of the design .
Question 24 :
The wheel of a motor cycle is of radius 35 cm. How many revolutions per minute must the wheel make so as to keep a speed of 66 km/h ?
Question 25 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b34273b230584979953.jpg' />
In the above figure, a square is inscribed in a circle of diameter d and another square is circumscribing the circle. Is the area of outer square 4 times the area of inner square ?
Question 26 :
Find the area of the major sector of a circle with radius 4 cm and of angle $30^{\circ}$.
Question 27 :
A circular pond is 17.5 m of diameter. It is surrounded by a 2 m wide path. Find the cost of constructing the path at the rate of Rs. 25 per $m^2$.
Question 28 :
If the sum of the circumferences of two circles with radii $R_1$ and $R_2$ is equal to the circumference of a circle of radius R, then
Question 29 :
Find the difference of the areas of two segments of a circle formed by a chord of length 5 cm subtending an angle of $90^{\circ}$ at the centre.
Question 30 :
The radii of two circles are 19 cm and 9 cm respectively. Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles.
Question 31 :
Tick the correct answer in the following and justify your choice. If the perimeter and the area of a circle are numerically equal, then the radius of the circle is
Question 32 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19baf273b2305849799f4.png' />
The above image 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 21 cm and each of the other bands is 10.5 cm wide. Find the area of the black scoring region.
Question 33 :
A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding minor segment.(Use $\pi$ =3.14)
Question 34 :
Area of a sector of central angle $200^{\circ}$ of a circle is $770\ cm^2$. Find the length of the corresponding arc of this sector.
Question 35 :
Area of the largest triangle that can be inscribed in a semi-circle of radius $r$ units is
Question 36 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b3d273b23058497995e.jpg' />
In the above figure, a floor of a room of dimensions $5\ m\times4\ m$ covered with circular tiles of diameters 50 cm each is shown. Find the area of the floor that remains uncovered with tiles.
Question 37 :
The diameters of front and rear wheels of a tractor are 80 cm and 2 m respectively. Find the number of revolutions that rear wheel will make in covering a distance in which the front wheel makes 1400 revolutions.
Question 38 :
If the sum of the areas of two circles with radii $R_1$ and $R_2$ is equal to the area of a circle of radius $R$, then
Question 39 :
To warn ships for underwater rocks, a lighthouse spreads a red coloured light over a sector of angle $80^{\circ}$ to a distance of 16.5 km . Find the area of the sea over which the ships are warned. (Use $\pi$= 3.14)
Question 40 :
The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle having area equal to the sum of the areas of the two circles.
Question 41 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bbc273b230584979a05.png' />
In the above figure , AB and CD are two diameters of a circle (with centre O) perpendicular to each other and OD is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region.
Question 42 :
The wheels of a car are of diameter 80 cm each. How many complete revolutions does each wheel make in 10 minutes when the car is travelling at a speed of 66 km per hour?
Question 43 :
On a square cardboard sheet of area 784 $cm^2$, four congruent circular plates of maximum size are placed such that each circular plate touches the other two plates and each side of the square sheet is tangent to two circular plates. Find the area of the square sheet not covered by the circular plates.
Question 44 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19baa273b2305849799ee.png' />
In the above figure, two circular flower beds have been shown on two sides of a square lawn ABCD of side 56 m . If the centre of each circular flower bed is the point of intersection O of the diagonals of the square lawn , find the sum of the areas of the lawn and the flower beds.
Question 45 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b3a273b23058497995a.jpg' />
In the above figure, arcs are drawn by taking vertices A, B and C of an equilateral triangle of side 10 cm to intersect the sides BC, CA and AB at their respective mid-points D, E and F. Find the area of the shaded region (Use $\pi=3.14$).
Question 46 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b3d273b23058497995f.jpg' />
In the above figure, an archery target formed by 3 concentric circles is shown which has three regions. If the diameters of the concentric circles are in the ratio 1: 2: 3, then find the ratio of the areas of three regions.
Question 47 :
A piece of wire 20 cm long is bent into the form of an arc of a circle subtending an angle of $60^{\circ}$ at its centre. Find the radius of the circle.
Question 48 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a48273b230584979913.jpeg' />
The above figure depicts an archery target marked with its five scoring regions from centre outwards as gold, red, blue, black and white. The diameter of the region representing gold score is 21 cm and each of the ofher bands is 10.5 cm wide. Find the area of white scoring region.
Question 49 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bb4273b2305849799fb.png' />
(As shown in the above figure)A round table cover has six equal designs . If the radius of the cover is 28 cm, find the cost of making the designs at the rate of Rs 0.35 per $cm^2$ . (Use $\sqrt{3}$ = 1.7)
Question 50 :
If $\theta$ is the angle (in degrees) of a sector of a circle of radius $r$, then area of the sector is
