10th Class Mathematics Areas Related to Circles Question Bank

done Assertion And Reason (MCQs) - Areas Related to Circles Total Questions - 18

• question_answer1)

  Directions (Q. Nos. 1 - 18): In the following questions, statement of Assertion (A) is followed by a statement of Reason R). Mark the correct choice as:

  Assertion (A): In a circle of radius \[\text{6 cm},\] the angle of a sector \[60{}^\circ \]. Then the area of the sector is \[18\frac{6}{7}c{{m}^{2}}\].

  Reason (R): Area of the circle with radius r is \[\pi {{r}^{2}}\].

  A)
  Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A) done clear
  B)
  Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A) done clear
  C)
  Assertion (A) is true but Reason (R) is false done clear
  D)
  Assertion (A) is false but Reason (R) is true done clear
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• question_answer2)

  Assertion (A): If the circumference of a circle is \[\text{176 cm},\]then its radius is\[\text{28 cm}\].

  Reason (R): Circumference \[=2\pi \times radius\]

  A)
  Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A) done clear
  B)
  Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A) done clear
  C)
  Assertion (A) is true but Reason (R) is false done clear
  D)
  Assertion (A) is false but Reason (R) is true done clear
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• question_answer3)

  Assertion (A): If the radius of a circle is \[\frac{7}{\sqrt{\pi }}cm,\] then the area of the circle is \[49\,c{{m}^{2}}\].

  Reason (R): If r is radius of a circle, then area of circle is \[2\pi r\].

  A)
  Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A) done clear
  B)
  Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A) done clear
  C)
  Assertion (A) is true but Reason (R) is false done clear
  D)
  Assertion (A) is false but Reason (R) is true done clear
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• question_answer4)

  Assertion (A): The radius of the wheel of a bus is\[\text{25 cm}\]. If the speed of the bus is \[\text{33 km}/\text{h},\] then number of revolutions made by wheel in 1 min is 250.

  Reason (R): Number of revolutions in one minute

  \[=\frac{\text{Distance covered in 1 min}}{\text{circumference}}\]

  A)
  Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A) done clear
  B)
  Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A) done clear
  C)
  Assertion (A) is true but Reason (R) is false done clear
  D)
  Assertion (A) is false but Reason (R) is true done clear
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• question_answer5)

  Assertion (A): The length of the minute hand of a clock is \[\text{7 cm}\]. The n the area swept by the minute hand in 5 minutes is \[12\frac{5}{6}c{{m}^{2}}\]

  Reason (R): The length of an arc of a sector of angle \[\theta \] and radius r is given by \[l=\frac{\theta }{360}\times 2\pi r\]

  A)
  Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A) done clear
  B)
  Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A) done clear
  C)
  Assertion (A) is true but Reason (R) is false done clear
  D)
  Assertion (A) is false but Reason (R) is true done clear
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• question_answer6)

  Assertion (A): A wire is looped in the form of a circle of radius\[\text{28 cm}\]. It is sent into a square. Then the area of the square is \[1936\,c{{m}^{2}}\].

  Reason (R): Angle described by a minute hand in 60 minutes\[=360{}^\circ \]

  A)
  Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A) done clear
  B)
  Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A) done clear
  C)
  Assertion (A) is true but Reason (R) is false done clear
  D)
  Assertion (A) is false but Reason (R) is true done clear
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• question_answer7)

  Assertion (A): Circular footpath of width \[2\,m\] is constructed at the rate of \[\text{Rs}.\text{2}0\text{ per }{{\text{m}}^{2}}\]around a circular park of radius\[\text{15}00\text{ m}\]. The total cost of construction of the footpath is \[\text{Rs}.\text{377}0\text{51}.\text{2}\].

  Reason (R): Area of the footpath \[=\pi ({{R}^{2}}-{{r}^{2}}),\] where R and rare outer and inner radii of the park respectively.

  A)
  Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A) done clear
  B)
  Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A) done clear
  C)
  Assertion (A) is true but Reason (R) is false done clear
  D)
  Assertion (A) is false but Reason (R) is true done clear
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• question_answer8)

  Assertion (A): The area of the quadrant of a circle having circumference of \[44cm\]is \[\frac{77}{2}c{{m}^{2}}\].

  Reason (R): The area of a sector of a circle of radius r with central angle x is \[\frac{x}{360{}^\circ }\times \pi {{r}^{2}}\].

  A)
  Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A) done clear
  B)
  Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A) done clear
  C)
  Assertion (A) is true but Reason (R) is false done clear
  D)
  Assertion (A) is false but Reason (R) is true done clear
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• question_answer9)

  Assertion (A): If the outer and inner diameter of a circular path is\[10m\]and \[6\,m\]then area of the path is \[16\pi {{m}^{2}}\].

  Reason (R):  If R and r be the radius of outer and inner circular path \[=\pi ({{R}^{2}}-{{r}^{2}})\].

  A)
  Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A) done clear
  B)
  Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A) done clear
  C)
  Assertion (A) is true but Reason (R) is false done clear
  D)
  Assertion (A) is false but Reason (R) is true done clear
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• question_answer10)

  Assertion (A): A bicycle wheel makes 5000 revolutions in covering \[11km\]. Then diameter of the wheel is \[35\,cm\].

  Reason (R): Area of segment of a circle is \[\frac{\theta }{360}\times \pi {{r}^{2}}-\frac{1}{2}{{r}^{2}}\sin \theta \]

  A)
  Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A) done clear
  B)
  Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A) done clear
  C)
  Assertion (A) is true but Reason (R) is false done clear
  D)
  Assertion (A) is false but Reason (R) is true done clear
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• question_answer11)

  Assertion (A): If the circumferences of two circles are in the ratio \[\text{1}:\text{3},\] then the ratio of their areas is \[1:9\].

  Reason (R): The area of a sector of a circle of radius r with sector angle \[\theta \] is \[\frac{\theta }{360{}^\circ }\times \pi {{r}^{2}}\].

  A)
  Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A) done clear
  B)
  Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A) done clear
  C)
  Assertion (A) is true but Reason (R) is false done clear
  D)
  Assertion (A) is false but Reason (R) is true done clear
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• question_answer12)

  Assertion (A): Area of the square inscribed in a circle of radius r is \[2{{r}^{2}}\,sq.\] units.

  Reason (R): Area of the major segment of a circle = area of the circle - Area of minor segment.

  A)
  Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A) done clear
  B)
  Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A) done clear
  C)
  Assertion (A) is true but Reason (R) is false done clear
  D)
  Assertion (A) is false but Reason (R) is true done clear
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• question_answer13)

  Assertion (A): If a wire of length \[\text{22 cm}\] is bent in the shape of a circle, then area of the circle so formed is \[\text{40 c}{{\text{m}}^{2}}\].

  Reason (R): Circumference of the circle = length of the wire.

  A)
  Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A) done clear
  B)
  Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A) done clear
  C)
  Assertion (A) is true but Reason (R) is false done clear
  D)
  Assertion (A) is false but Reason (R) is true done clear
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• question_answer14)

  Assertion (A): If the perimeter of a sector of a circle of radius \[\text{5}.\text{6 cm}\] is \[\text{27}.\text{2 cm},\] then the area of the sector is\[\text{44}.\text{8 c}{{\text{m}}^{\text{2}}}\].

  Reason (R): The area of a sector of a circle of radius r with central angle \[\theta \] is \[\frac{\theta }{360{}^\circ }\times \pi r\].

  A)
  Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A) done clear
  B)
  Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A) done clear
  C)
  Assertion (A) is true but Reason (R) is false done clear
  D)
  Assertion (A) is false but Reason (R) is true done clear
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• question_answer15)

  Assertion (A): A sector is cut from a circle of radius\[\text{42 cm}\]. The central angle of the sector is \[150{}^\circ \]. The perimeter of the sector is\[\text{194 cm}\]

  Reason (R): \[\text{Perimeter of sector}=2\,(radius)+\] \[\text{Length of corresponding arc of sector}\]

  A)
  Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A) done clear
  B)
  Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A) done clear
  C)
  Assertion (A) is true but Reason (R) is false done clear
  D)
  Assertion (A) is false but Reason (R) is true done clear
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• question_answer16)

  Assertion (A): If the circumference of two circles are in the ratio \[2:e\] then ratio of their areas is\[4:9\].

  Reason (R): The circumference of a circle of radius r is \[2\pi r\] and its area is \[\pi {{r}^{2}}\] .

  A)
  Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A) done clear
  B)
  Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A) done clear
  C)
  Assertion (A) is true but Reason (R) is false done clear
  D)
  Assertion (A) is false but Reason (R) is true done clear
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• question_answer17)

  Assertion (A): In the figure, \[{{C}_{1}}\] and \[{{C}_{2}}\]are two circles with radii \[\text{7 cm}\] and \[\text{5 cm}\] respectively, then area of shaded portion is \[24\,\pi \,c{{m}^{2}}\] .

  Reason (R): When two circles touch internally, the distance between their centres is equal to sum of their radii.

  A)
  Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A) done clear
  B)
  Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A) done clear
  C)
  Assertion (A) is true but Reason (R) is false done clear
  D)
  Assertion (A) is false but Reason (R) is true done clear
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• question_answer18)

  Assertion (A): In the given figure, if arcs are drawn by taking vertices A, B and C of an equilateral triangle of side 8 cm, to intersect the sides BC, CA and AB at their respective mid-points D, E and F, then are of the shaded  region is\[25.12\,c{{m}^{2}}\].

  Reason (R): Area of shaded region\[=\text{Area of }\Delta \text{ABC}-\text{Area of 3 equal sectors}.\]

  A)
  Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A) done clear
  B)
  Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A) done clear
  C)
  Assertion (A) is true but Reason (R) is false done clear
  D)
  Assertion (A) is false but Reason (R) is true done clear
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