Question 1 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b3c273b23058497995d.jpg' />
In the above figure, ABCD is a trapezium with $AB\ \parallel\ DC$, AB = 18 cm, DC = 32 cm and distance between AB and DC is 14 cm. If arcs of equal radii 7 cm with centres A, B, C and D have been drawn, then find the area of the shaded region.
Question 2 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b3f273b230584979961.jpg' />
In the above figure, a circle is inscribed in a square of side 5 cm and another circle is circumscribing the square. Is it true that area of the outer circle is two times the area of the inner circle ?
Question 3 :
Area of a sector of angle p (in degrees) of a circle with radius R is
Question 4 :
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 5 :
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 6 :
It is proposed to build a single circular park equal in area to the sum of areas of two circular parks of diameters 16 m and 12 m in a locality. The radius of the new park would be
Question 7 : <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 8 : <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 9 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b41273b230584979963.jpg' />
In the above figure, A Triangle ABC with vertices A, B and C as centres, arcs are drawn with radii 5 cm each. If AB = 14 cm, BC = 48 cm and CA = 50 cm, then find the area of the shaded region.
Question 10 :
Find the area of a quadrant of a circle whose circumference is 22 cm.
Question 11 :
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 12 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b39273b230584979959.jpg' />
In the above figure, if arcs are drawn with centres A, B, C and D intersects in pairs at mid-points P, Q, R and S of the sides AB, BC, CD and DA, respectively of a square ABCD. Find the area of the shaded region (Use $\pi=3.14$).
Question 13 :
Find the area of the segment of a circle of radius 12 cm whose corresponding sector has a central angle of $60^{\circ}$ (Use $\pi=3.14$).
Question 14 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bb6273b2305849799fd.png' />
Find the area of the shaded region in the above figure , if radii of the two concentric circles with centre O are 7 cm and 14 cm respectively and $\angle AOC$=$40^{\circ}$.
Question 15 : <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 16 :
The area of the square that can be inscribed in a circle of radius 8 cm is
Question 17 :
The area of a square inscribed in a circle of diameter $p\ cm$ is $p^2\ cm^2$. Is it true or false?
Question 18 :
If $\theta$ is the angle (in degrees) of a sector of a circle of radius $r$, then area of the sector is
Question 19 :
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 20 :
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 21 :
Find the area of the minor segment of a circle of radius 14 cm, when the angle of the corresponding sector is $60^{\circ}$ .
Question 22 : <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 23 :
Find the difference of tha areas of a sector of an angle $120^{\circ}$ and its corresponding major sector of a circle of radius 21 cm.
Question 24 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bae273b2305849799f3.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 blue scoring region.
Question 25 :
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 26 :
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 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 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 29 :
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 30 :
The area of a circular playground is 22176 $m^2$. Find the cost of fencing this ground at the rate of Rs. 50 per metre.
Question 31 :
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 32 : <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 33 :
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 34 :
Area of the largest triangle that can be inscribed in a semi-circle of radius $r$ units is
Question 35 :
If the perimeter and the area of a circle are numerically equal, then the radius of the circle is
Question 36 :
The numerical value of the area of a circle is greater than the numerical value of its circumference. Is it true or false?
Question 37 : <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 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 : <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 40 :
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 41 :
Find the area of the minor sector of a circle with radius 4 cm and of angle $30^{\circ}$.
Question 42 :
The cost of fencing a circular field at the rate of Rs 24 per metre is Rs 5280. The field is to be ploughed at the rate of Rs 0.50 per $m^2$ . Find the cost of ploughing the field (Take $\pi$= $\frac{22}{7}$ ).
Question 43 :
A chord of a circle of radius 15 cm subtends an angle of $60^{\circ}$ at the centre. Find the area of the corresponding minor segment of the circle. (Use $\pi$ = 3.14 and $\sqrt{3}$ = 1.73)
Question 44 :
A chord of a circle of radius 12 cm subtends an angle of $120^{\circ}$ at the centre. Find the area of the corresponding segment of the circle.(Use $\pi$= 3.14 and $\sqrt{3}$ = 1.73)
Question 45 :
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 46 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bb3273b2305849799f9.png' />
In the above figure a brooch is made with silver wire in the form of a circle with diameter 35 mm . The wire is also used in making 5 diameters which divide the circle into 10 equal sectors . Find the area of each sector of the brooch.
Question 47 : <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 48 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bc0273b230584979a0b.png' />
In the above figure , AB and CD are respectively arcs of two concentric circles of radii 21 cm and 7 cm and centre O . If $\angle AOB$=$30^{\circ}$ , find the area of the shaded region.
Question 49 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19baf273b2305849799f5.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 white scoring region.
Question 50 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bb8273b230584979a00.png' />
In the above figure , find the area of the shaded region , where a circular arc of radius 6 cm has been drawn with vertex O of an equilateral triangle OAB of side 12 cm as centre.
