Vardaan Learning Institute

Chapter Practice Sheet: Areas Related to Circles

Class: 10 (CBSE) Subject: Mathematics Max. Marks: 50
SECTION A: OBJECTIVE TYPE QUESTIONS (1 Mark Each)
1. 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:
  1. $R_1 + R_2 = R$
  2. $R_1^2 + R_2^2 = R^2$
  3. $R_1 + R_2 < R$
  4. $R_1^2 + R_2^2 < R^2$
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2. Area of a sector of angle p (in degrees) of a circle with radius R is:
  1. $\frac{p}{180} \times 2\pi R$
  2. $\frac{p}{180} \times \pi R^2$
  3. $\frac{p}{360} \times 2\pi R$
  4. $\frac{p}{720} \times 2\pi R^2$
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3. The length of the minute hand of a clock is 14 cm. The area swept by the minute hand in 5 minutes is:
  1. $154/3$ cm$^2$
  2. $44/3$ cm$^2$
  3. $154$ cm$^2$
  4. $77$ cm$^2$
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4. If the perimeter of a circle is equal to that of a square, then the ratio of their areas is:
  1. 22:7
  2. 14:11
  3. 7:22
  4. 11:14
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5. A wheel makes 1000 revolutions in covering a distance of 88 km. The radius of the wheel is:
  1. 14 m
  2. 24 m
  3. 7 m
  4. 12 m
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6. A race track is in the form of a ring whose inner and outer circumferences are 437 m and 503 m respectively. The width of the track is:
  1. 10.5 m
  2. 20.5 m
  3. 21 m
  4. 10 m
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7. The area of a circle that can be inscribed in a square of side 6 cm is:
  1. $36\pi$ cm$^2$
  2. $18\pi$ cm$^2$
  3. $12\pi$ cm$^2$
  4. $9\pi$ cm$^2$
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8. If the circumference of a circle and the perimeter of a square are equal, then:
  1. Area of the circle = Area of the square
  2. Area of the circle > Area of the square
  3. Area of the circle < Area of the square
  4. Nothing definite can be said about the relation between the areas of the circle and square.
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9. The area of a sector of a circle with radius 6 cm if angle of the sector is $60^\circ$ is:
  1. 132/7 cm$^2$
  2. 142/7 cm$^2$
  3. 152/7 cm$^2$
  4. 122/7 cm$^2$
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10. Assertion (A): The length of the minute hand of a clock is 7 cm. The area swept by the minute hand in 30 minutes is 77 cm$^2$.
Reason (R): The length of an arc of a sector of angle $\theta$ and radius $r$ is given by $l = \frac{\theta}{360} \times 2\pi r$.
  1. Both A and R are true and R is the correct explanation of A.
  2. Both A and R are true but R is not the correct explanation of A.
  3. A is true but R is false.
  4. A is false but R is true.
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SECTION B: SHORT ANSWER TYPE QUESTIONS (2 Marks Each)
11. Find the area of a quadrant of a circle whose circumference is 22 cm.
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12. A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the minor segment. (Use $\pi = 3.14$)
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13. In a circle of radius 21 cm, an arc subtends an angle of $60^{\circ}$ at the center. Find the length of the arc.
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14. 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.
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SECTION C: SHORT ANSWER TYPE II QUESTIONS (3 Marks Each)
15. Find the area of the shaded region in the figure, if ABCD is a square of side 14 cm and APD and BPC are semicircles. Question 7 Figure
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16. Calculate the area of the designed region common between the two quadrants of circle of radius 8 cm each. Question 8 Figure
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17. 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 9 Figure
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18. 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.
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19. 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 as shown in the figure. Find the area of the remaining portion of the square.
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20. A horse is tied to a peg at one corner of a square shaped grass field of side 15m by means of a 5m long rope. Find (i) the area of that part of the field in which the horse can graze. (ii) the increase in the grazing area if the rope were 10m long instead of 5m. (Use $\pi = 3.14$)
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SECTION D: LONG ANSWER TYPE QUESTIONS (5 Marks Each)
21. In the figure, ABCD is a trapezium with AB || 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 of the figure.
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22. OACB is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the (i) quadrant OACB, (ii) shaded region.
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SECTION E: CASE STUDY (4 Marks)
23. Case Study: Car Wipers
A car has two wipers which do not overlap. Each wiper has a blade of length 25 cm sweeping through an angle of $115^{\circ}$.

(i) Calculate the total area cleaned at each sweep of the blades. (2 Marks)
(ii) What is the area of the sector formed by one wiper? (1 Mark)
(iii) If the angle was $90^{\circ}$, what would be the area swept by one blade? (1 Mark)
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