Question 1 :
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 2 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bc0273b230584979a0a.png' />
In the above figure , a square OABC is inscribed in a quadrant OPBQ . If OA = 20 cm , find the area of the shaded region . (Use $\pi$ = $\frac{22}{7}$)
Question 3 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b37273b230584979956.jpg' />
In the above figure, AB is the diameter of the circle, AC = 6 cm and BC = 8 cm. Find the area of the shaded region (Use $\pi=3.14$).
Question 4 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a46273b230584979910.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 blue scoring region.
Question 5 : <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 6 : <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 7 :
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 8 : <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 9 : <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 10 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b3b273b23058497995b.jpg' />
In the above figure, arcs are drawn with radii 14 cm each and with centres P, Q and R. Find the area of the shaded region.
Question 11 :
Find the number of revolutions made by a circular wheel of area $1.54\ m^2$ in rolling a distance of 176 m.
Question 12 :
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 13 : <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 14 :
If $\theta$ is the angle (in degrees) of a sector of a circle of radius $r$, then area of the sector is
Question 15 :
Is the area of the circle inscribed in a square of side $a\ cm$, $\pi a^2\ cm^2$ ?
Question 16 : <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 17 :
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 18 : <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 19 : <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 20 :
The numerical value of the area of a circle is greater than the numerical value of its circumference. Is it true or false?
Question 21 : <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 22 : <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 23 :
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 24 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a48273b230584979912.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 black scoring region.
Question 25 :
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 26 :
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 27 : <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 28 : <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 29 :
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 30 :
Four circular cardboard pieces of radii 7 cm are placed on a paper in such a way that each piece touches other two pieces. Find the area of the portion enclosed between these pieces.
Question 31 :
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 32 : <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 33 :
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 34 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b38273b230584979957.jpg' />
In the above figure, dimensions are given. Find the area of the shaded field.
Question 35 :
Find the area of the minor sector of a circle with radius 4 cm and of angle $30^{\circ}$.
Question 36 :
Find the area of the major sector of a circle with radius 4 cm and of angle $30^{\circ}$.
Question 37 :
If the perimeter of a circle is equal to that of a square, then the ratio of their areas is
Question 38 : <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 39 : <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 40 :
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 41 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b35273b230584979954.jpg' />
In the above figure, a square of diagonal 8 cm is inscribed in a circle. Find the area of the shaded region.
Question 42 :
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 43 : <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 44 :
The area of a segment of a circle is less than the area of its corresponding sector. Is it true or false?
Question 45 : <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 46 : <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 47 : <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 48 :
Find the area of a quadrant of a circle whose circumference is 22 cm.
Question 49 :
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 50 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bb7273b2305849799fe.png' />
In the above figure , find the area of the shaded region if ABCD is a square of side 14 cm and APD and BPC are semicircles.
