Class 10 - Arihant - All in one (Math) - Areas Related to CirclesContact Number: 9667591930 / 8527521718

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1.

The radii of two circles are 13 cm and 6 cm. respectively. Find the radius of the circles which has the circumference equal to the sum of the circumferences of the two circles.

2.

The cost of fencing a circular field at the rate of ₹ 24 per meter is ₹ 5280. The field is to be ploughed at the rate of ₹ 0.50 per ${\mathrm{m}}^{2}.$ Find the cost of ploughing the field. $\left[\mathrm{Take},\mathrm{\pi}=22/7\right]$

3.

The circular footpath of width 2 m is constructed at the rate of ₹ 20 per ${\mathrm{m}}^{2}$ around a circular park of radius 1500 m. Find the total cost of construction of the footpath. $\left[\mathrm{Take},\mathrm{\pi}=3.14\right]$

4.

If the area of a semi-circular field is 30800 sq. m, then find the perimeter of the field.

5.

the radius of the wheel of a bus is 25 cm. If the speed of the bus is 33 km/h, then how many revolutions will the wheel make in 1 min?

6.

the short and long hands of a clock are 6 cm and 8 cm long respectively, find the sum of the distance travelled by their tips in 1 day.

$\left[\mathrm{Take},\mathrm{\pi}=22/7\right]$

7.

The shaded area in the adjacent figure between the circumference of two concentric circles is $346.4{\mathrm{cm}}^{2}.$ The circumference of the inner circle is 88 cm. calculate the radius of the outer circle.

8.

the ratio of the outer and inner circumference of a circular path is 23:22. If the path is 5 m wide, then find the diameter of the inner circle.

9.

Two circles touch each other externally. The sum of their areas is 130$\mathrm{\pi}$ ${\mathrm{cm}}^{2}$ and the distance between their centers is 14 cm. Find the radii of the circles.

10.

A boy is cycling such that the wheels of the cycle are making 140 revolutions per minute. If the diameter of the wheel is 60 cm, then find the speed per hour with which the boy is cycling.

11.

If the perimeter of a circle is equal to that of a square, then find the ratio of their areas.

12.

Two parallel lines touch the circle at points A and B, respectively. If the area of the circle is 25$\mathrm{\pi}{\mathrm{cm}}^{2}$, then find the length of AB.

13.

A wire when bent in the form of a square enclose an area 121 sq cm. If the wire was bent in the form of a circle, then find the area enclosed by the circle. $\left[\mathrm{Take},\mathrm{\pi}=\frac{22}{7}\right]$

14.

the length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in one minute. $\left[\mathrm{Take},\mathrm{\pi}=\frac{22}{7}\right]$

15.

In a circle of radius 28 cm, an arc subtends an angle of $45\xb0$ at the center. Find the length of the arc and using it, find the area of the sector.

16.

$\mathrm{find}\mathrm{the}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{segment}\mathrm{AYB},\mathrm{if}\mathrm{radius}\mathrm{of}\mathrm{the}\mathrm{circle}\mathrm{is}21\mathrm{cm}\mathrm{and}\angle \mathrm{AOB}=120\xb0.\left[\mathrm{Tale},\mathrm{\pi}=\frac{22}{7}\right]$

17.

$\mathrm{Find}\mathrm{the}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{sector}\mathrm{of}\mathrm{a}\mathrm{circle}\mathrm{with}\mathrm{radius}4\mathrm{cm}\mathrm{and}\mathrm{of}\mathrm{angle}30\xb0.\mathrm{Also},\mathrm{find}\mathrm{the}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{corresponding}\mathrm{major}\mathrm{sector}.$

18.

the length of an hour hand of a clock is 7 cm. Find the area swept by the hour hand in one hour.

19.

The minute hand of a clock is 12 cm long. Find the area of the face of the clock described by the minute hand between 9 am and 9:35 cm.

20.

In a circle of radius 21 cm, an arc subtends an angle of $60\xb0$ at the center. Find the length of the arc.

21.

In the given figure. O is the center of the circle with a radius equal to 14 cm. The length of the arc AB = 13.2 cm. Find the area of the shaded sector of the circle.

22.

Area of a sector of a circle of radius 36 cm is 54$\mathrm{\pi}{\mathrm{cm}}^{2}.$ Find the length of the corresponding arc of the sector.

23.

A cow is tied with a rope of length 14 m at the corner of a rectangular field of dimensions 20 m x 16 m. Find the area of the field in which the cow can graze.

24.

25.

find the area of the shaded region in the figure as shown below where ABCD is a square of sides 12 cm.

26.

Find the area of shaded design in the given figure, where ABCD is a square of side 10 cm and semi-circles are drawn with each of the sides as diameter. $\left[\mathrm{Take},\mathrm{\pi}=3.14\right]$

27.

In the given figure, sectors of two concentric circles of radii 7 cm and 3.5 cm are shown. Find the area of the shaded region.

28.

$\mathrm{In}\mathrm{figure},\mathrm{AOB}\mathrm{is}\mathrm{a}\mathrm{flower}\mathrm{bed}\mathrm{in}\mathrm{the}\mathrm{shape}\mathrm{of}\mathrm{a}\mathrm{sector}\mathrm{of}\mathrm{a}\mathrm{circle}\mathrm{of}\mathrm{radius}40\mathrm{m}\mathrm{and}\angle \mathrm{AOB}=60\xb0.\mathrm{Also},\mathrm{a}15\mathrm{m}\mathrm{wide}\mathrm{concrete}\mathrm{track}\mathrm{is}\phantom{\rule{0ex}{0ex}}\mathrm{made}\mathrm{as}\mathrm{shown}\mathrm{in}\mathrm{the}\mathrm{figure}.\mathrm{Flower}\mathrm{bed}\mathrm{is}\mathrm{made}\mathrm{at}\mathrm{the}\mathrm{rate}\mathrm{of}\u20b92.40\mathrm{per}{\mathrm{m}}^{2}\mathrm{and}\mathrm{rate}\mathrm{of}\mathrm{making}\mathrm{the}\mathrm{concrete}\mathrm{track}\mathrm{is}\u20b920\mathrm{per}{\mathrm{m}}^{2}.\phantom{\rule{0ex}{0ex}}\mathrm{Find}\mathrm{the}\mathrm{total}\mathrm{amount}\mathrm{spent}\mathrm{for}\mathrm{the}\mathrm{job}.\left[\mathrm{Take},\mathrm{\pi}=3.14\right]$

29.

A memento is made as shown in the figure. Its base PBCR is silver plated from the front side at the rate of ₹ 20 per ${\mathrm{cm}}^{2}$. Find the total cost of the silver plating. $\left[\mathrm{Take},\mathrm{\pi}=\frac{22}{7}\right]$

30.

Find the area of the shaded region in the figure, if AC = 20 cm, AB = 15 cm and O is the center of the circle. $\left[\mathrm{Take},\mathrm{\pi}=\frac{22}{7}\right]$

31.

In the adjoining figure, OACBO represents a quadrant of a circle of radius 4.5 cm with center O. Calculate the area of the shaded portion. $\left[\mathrm{Take},\mathrm{\pi}=22/7\right]$

32.

A paper is in the form of a rectangle ABCD in which AB = 20 cm and BC = 14 cm. A semi-circular portion with BC as the diameter is cut-off. Find the area of the remaining part.

33.

From each of the two opposite corners of a square of side 8 cm, a quadrant of a circle of radius 1.4 cm is cut. Another circle of radius 4.2 cm is also cut from the center as shown in the figure. Find the area of the remaining (shaded) portion of the square. $\left[\mathrm{Take},\mathrm{\pi}=22/7\right]$

34.

a square park has a side of 100 m. At each corner of the park, there is a flower bed in the form of a quadrant of radius 14 m as shown in the figure below. find the area of the remaining part of the park.

35.

In the given figure, ABCD is a square of side 7 cm and A, B, C, and D are the center of equal circles touching externally in pairs. Find the area of the shaded region.

36.

In the given figure, the diameter AB is 12 cm long. AB is trisected at points P and Q. Find the area of the shaded region.$\left[\mathrm{Take}\mathrm{\pi}=3.14\right]$

37.

On a circular table cover of radius 42 cm. a design is formed by a girl leaving an equilateral AABC in the middle as shown in the figure. It was decided that the payment to the girl be made proportional to the covered area cf the design. Find the covered area of the design. $\left[\mathrm{take},\sqrt{3}=\text{'}1.73\mathrm{and}\mathrm{\pi}=\frac{22}{7}\right]$

38.

There are three semi-circles A, B, and C having diameter 3 cm each and another semi-circle E having a circle D with diameter 45 cm as shown in the figure below. Find the area of the shaded region.

39.

In the given, PQRS is a rectangle of length $10\sqrt{2}$and breadth $5\sqrt{2}$ cm. If PEO is an isosceles triangle inscribed in the semi-circle with diameter PQ, then find the area of the shaded region.

40.

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

41.

The given figure 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 the Gold score is 21 cm and each of the other bands is 10.5 cm vide. Find the area of each of the five scoring regions.

42.

The wheels of a car are of diameter 80 cm each. How many complete revolutions does each wheel make in 10 min when the car is traveling at a speed of 66 km per h?

43.

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

1. 2 units

2. $\mathrm{\pi}$ units

3. 4 units

4. 7 units

44.

Find the area of a sector of a circle with radius 6 cm, if angle of the sector is $60\xb0.$

45.

Find the area of a quadrant of a circle whose circumference is 22 cm.

46.

A chord of a circle of radius 10 cm subtends a right angle at the center. Find the area of the corresponding

(i) minor segment.

(ii) major sector. $\left[\mathrm{Take},\mathrm{\pi}=3.14\right]$

47.

In a circle of radius 21 cm, an arc subtends an angle of $60\xb0$ at the center. Find

(i) The length of the arc

(ii) Area of the segment formed by the arc.

(iii) Area of the segment formed by the corresponding chord.

48.

A chord of a circle of radius 15 cm subtends an angle of $60\xb0$ at the center. Find the areas of the corresponding minor and major segments of the circle. $\left[\mathrm{Take},\mathrm{\pi}=3.14\mathrm{and}\sqrt{3}=1.73\right]$

49.

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 (see the figure). Find

(i) The area of the part of the field in which the horse can graze.

(ii) The increase in the grazing area if the rope was 10m long instead of 5m. $\left[\mathrm{Take},\mathrm{\pi}=3.14\right]$

50.

A brooch is made with silver wire in the form of a circle with a diameter of 35 mm. The wire is also used in making 5 diameters which divide the circle into 10 equal sectors as shown in the figure. Find

(i) the total length of the silver wire required.

(ii) the area of each sector of the brooch.

51.

An umbrella has g ribs that are equally spaced (see the figure). Assuming umbrella to be a flat circle of radius '15 cm, find the between the two consecutive ribs of the umbrella.

52.

A car has two wipers that do not overlap. Each wiper has a blade of length 25 cm sweeping Through an angle of $115\xb0.$ Find the total area cleaned at each sweep of the blades.

53.

To warn ships for underwater rocks, a lighthouse spreads a red-colored light over a sector of an angle of $80\xb0$ to a distance of 16.5 km. Find the area of the sea over which the ships are warned. $\left[\mathrm{Take},\mathrm{\pi}=3.14\right]$

54.

A round table cover has six equal design as shown in the figure. If the radius of the cover is 28 cm, find the cost of making the designs at the rate of ₹ 0.35 per ${\mathrm{cm}}^{2}.$ $\left[\mathrm{Take},\sqrt{3}=1.7\right]$

55.

Find the area of the shaded region in the given figure, if PQ = 24 cm, PR = 7 cm, and O is the center of the circle.

56.

Find the area of the shaded region in the figure, if radii of the two concentric circles with center O are 7 cm and 14 cm respectively and $\angle \mathrm{AOC}=40\xb0.$

57.

Find the area of the shaded region in the figure, if ABCD is a square of side 14 cm and APD and BPC are semi-circles.

58.

Find the area of the shaded region in the figure, where a circular arc of radius 6 cm has been drawn with vertex O of an equilateral triangle OAB of sides 12 cm as the center.