Question 1 :
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 2 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bab273b2305849799ef.png' />
Find the area of the shaded region in the above figure, where ABCD is a square of side 14 cm.
Question 3 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bad273b2305849799f1.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 gold scoring region.
Question 4 :
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 5 :
The perimeter of a square circumscribing a circle of radius a cm is 8a cm . Is it true or false?
Question 6 :
In a circle of radius 21 cm , an arc subtends an angle of $60^{\circ}$ at the centre. Find the length of the arc.
Question 7 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bb1273b2305849799f7.png' />
(As shown in the abovefigure)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 increase in the grazing area if the rope were 10 m long instead of 5 m. (Use $\pi$= 3.14)
Question 8 :
Three circles each of radius 3.5 cm are drawn in such a way that each of them touches the other two. Find the area enclosed between these circles.
Question 9 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bc2273b230584979a0d.png' />
From the above image , calculate the area of the designed region common between the two quadrants of circles of radius 8 cm each.
Question 10 :
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 11 :
In a circle of radius 21 cm, an arc subtends an angle of $60^{\circ}$ at the centre. Find area of the segment formed by the corresponding chord.
Question 12 :
The wheels of a car are of diameter 80 cm. How many complete revolutions does each wheel make in 10 minutes when the car is travelling at a speed of 66 km per h?
Question 13 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b38273b230584979958.jpg' />
In the above figure, dimensions are given. Find the area of the shaded region.
Question 14 :
Find the number of revolutions made by a circular wheel of area $1.54\ m^2$ in rolling a distance of 176 m.
Question 15 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bb7273b2305849799ff.png' />
(As shown in the above image)From each corner of a square of side 4 cm a quadrant of a circle of radius 1 cm is cut and also a circle of diameter 2 cm is cut . Find the area of the remaining portion of the square.
Question 16 :
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 17 : <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 18 :
If the areas of two sectors of two different circles are equal, then their corresponding arc lengths will be equal. Is it true or false?
Question 19 :
If the perimeter and the area of a circle are numerically equal, then the radius of the circle is
Question 20 : <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 21 :
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 the three animals.
Question 22 :
Find the diameter of the circle whose area is equal to the sum of the areas of the two circles of diameters 20 cm and 48 cm.
Question 23 :
If the circumference of a circle and perimeter of a square are equal, then
Question 24 :
If the circumferences of two circles are equal, then their areas are also equal. Is it true or false?
Question 25 : <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 26 :
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 27 : <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 28 :
Find the area of a sector of a circle of radius 21 cm and central angle $120^{\circ}$ .
Question 29 :
Find the area of a sector of a circle with radius 6 cm if angle of the sector is $60^{\circ}$.
Question 30 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b3e273b230584979960.jpg' />
In the above figure, dimensions are given. Find the area of the shaded region.
Question 31 :
Find the area of the sector of a circle of radius 5 cm, if the corresponding arc length is 3.5 cm.
Question 32 : <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 33 :
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 34 :
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 35 : <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 36 : <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 37 :
The areas of two sectors of two different circles with equal corresponding arc lengths are equal. Is it true or false?
Question 38 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bbf273b230584979a09.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 shaded region.
Question 39 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a45273b23058497990f.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 each of the gold scoring region.
Question 40 :
The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm is
Question 41 :
A circular park is surrounded by a road 21 m wide. If the radius of the park is 105 m, find the area of the road.
Question 42 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19ba9273b2305849799ed.png' />
Find the area of the segment AYB shown in the above image, if radius of the circle is 21 cm and $\angle AOB$ = $120 ^{\circ}$. (Use $\pi$= $\frac{22}{7}$ )
Question 43 : <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 44 :
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 45 :
If the area of a circle is $154 cm^2$, then its perimeter is
Question 46 :
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 47 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bac273b2305849799f0.png' />
Find the area of the shaded design in the above figure, where ABCD is a square of side 10 cm and semicircles are drawn with each side of the square as diameter. (Use $\pi$= 3.14)
Question 48 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bbb273b230584979a04.png' />
The above figure depicts a racing track whose left and right ends are semicircular.The distance between the two inner parallel line segments is 60 m and they are each 106 m long. If the track is 10 m wide , find the area of the track.
Question 49 :
Is the area of the largest circle that can be drawn inside a rectangle of length $a\ cm$ and breadth $b\ cm$ $\left(a>b\right)$ is $\pi\ b^2\ cm^2$ ?
Question 50 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bba273b230584979a02.png' />
In the above figure , ABCD is a square of side 14 cm. With centres A, B, C and D, four circles are drawn such that each circle touch externally two of the remaining three circles. Find the area of the shaded region.
