10th Class Mathematics Areas Related to Circles Question Bank

done Areas Related to Circles Total Questions - 25

• question_answer1)
  O is the centre of a circle of diameter 4 cm and OABC is a square, if the shaded area is \[\frac{1}{3}\] area of the square, then the side of the square is _____.
  A)
   \[\pi \sqrt{3}\]                         done clear
  B)
   \[\sqrt{3\pi }\]                         done clear
  C)
   \[3\sqrt{\pi }\]                         done clear
  D)
   \[3\pi \]            done clear
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• question_answer2)
              A steel wire when bent in the form of a square encloses an area of 121 sq. cm. If the same wire is bent into the form of a circle, find the area of the circle. [use \[\pi =\frac{22}{7}\]]                           
  A)
   \[44\text{ }c{{m}^{2}}\]         done clear
  B)
         \[308\text{ }c{{m}^{2}}\]      done clear
  C)
                      \[77\text{ }c{{m}^{2}}\]         done clear
  D)
         \[154\text{ }c{{m}^{2}}\]     done clear
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• question_answer3)
  In given figure, ABC is a triangle right- angled at B, with AB = 14 cm and BC = 24 cm. With the vertices A, B and C as centres, arcs are drawn each of radius 7 cm. Find the area of the shaded region. [Use \[\pi =\frac{22}{7}\]]                        
  A)
   \[91\text{ }c{{m}^{2}}\]                 done clear
  B)
  \[95\,c{{m}^{2}}\]              done clear
  C)
                                  \[97\,c{{m}^{2}}\]             done clear
  D)
        \[88\,c{{m}^{2}}~\]       done clear
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• question_answer4)
  If the difference between the area of a regular hexagonal plot and the area of a circular swimming tank circumscribed in it is\[26.705\text{ }{{m}^{2}}\]. Find the radius of the circular swimming tank. \[(\pi =3.143,\,\,\sqrt{3}=1.732)\]
  A)
   4 cm                           done clear
  B)
   7 cm               done clear
  C)
   11 cm                         done clear
  D)
   9 cm done clear
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• question_answer5)
  The inner circumference of a circular track is \[24\pi \,\,m\]. The track is 2 m wide from everywhere. The quantity of wire required to surround the path completely is ___
  A)
   80 m               done clear
  B)
   81 m   done clear
  C)
   82 m           done clear
  D)
          88 m done clear
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• question_answer6)
  The areas of two concentric circles are \[962.5\text{ }c{{m}^{2}}\]and \[1386\text{ }c{{m}^{2}}\]respectively. The width of the ring is _____.
  A)
   \[3.4\text{ }cm\]                     done clear
  B)
   \[3.5\text{ }cm\]                     done clear
  C)
   \[3.2\text{ }cm\]          done clear
  D)
          \[3.1\text{ }cm\] done clear
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• question_answer7)
  A chord of a circle subtends an angle of \[{{60}^{o}}\] at the centre. If the length of the chord is 100 cm, find the area of the major segment.
  A)
   \[30720.5\,c{{m}^{2}}\]     done clear
  B)
   \[31021.42\,c{{m}^{2}}\] done clear
  C)
         \[30391.7\,c{{m}^{2}}\]    done clear
  D)
          \[30520.61\,c{{m}^{2}}\] done clear
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• question_answer8)
  A park is in the form of a rectangle\[120\text{ }m\times 100\text{ }m\]. In the centre of the park, there is a circular lawn as shown in the figure. The area of the park excluding the lawn is\[8700\text{ }{{m}^{2}}\]. Find the radius of the circular lawn. \[\left( Use\,\,\pi =\frac{22}{7} \right)\]
  A)
   \[32.4\text{ }m\]                     done clear
  B)
   \[36.4\text{ }m\]            done clear
  C)
          \[32.6\,m\]           done clear
  D)
         \[39.4\text{ }m\]         done clear
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• question_answer9)
  Find the area of a ring whose outer and inner radii are respectively 23 cm and 12 cm.
  A)
   \[1125\text{ }c{{m}^{2}}\]             done clear
  B)
   \[1321\text{ }c{{m}^{2}}\]    done clear
  C)
                      \[1210\,\,c{{m}^{2}}\]      done clear
  D)
          \[1225\,\,c{{m}^{2}}\]        done clear
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• question_answer10)
  AB is a line segment of length 4 cm. P is the mid-point of AB. Circles are drawn with A, P and B as centres and radii AP = PB (see figure). The area of the shaded portion (in\[c{{m}^{2}}\]) is _____.    
  A)
   \[6\sqrt{3}\]                done clear
  B)
   \[2\pi -6\sqrt{3}\]         done clear
  C)
         \[2\pi -3\sqrt{3}\]         done clear
  D)
         \[3\sqrt{3}\] done clear
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• question_answer11)
  The perimeter of a sector of a circle of radius \[5.2\text{ }cm\]is\[16.4\text{ }cm\]. The area of the sector is _____.                 
  A)
   \[15.1\text{ }c{{m}^{2}}\]              done clear
  B)
   \[15.5\text{ }c{{m}^{2}}\]     done clear
  C)
                      \[15.6\,c{{m}^{2}}\]       done clear
  D)
          \[15.9\,c{{m}^{2}}\]     done clear
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• question_answer12)
  Circle \[{{C}_{2}}\] passes through the centre of circle \[{{C}_{1}}\]and is tangential to it. If the area of \[{{C}_{1}}\]is \[4\text{ }c{{m}^{2}},\] then the area of \[{{C}_{2}}\] is _____.
  A)
   \[8\,c{{m}^{2}}\]                            done clear
  B)
   \[8\,\sqrt{\pi \,}c{{m}^{2}}\]          done clear
  C)
   \[16\,c{{m}^{2}}\]        done clear
  D)
          \[16\sqrt{\pi }\,c{{m}^{2}}\] done clear
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• question_answer13)
  In the given figure, the area of the shaded region is ___.  
  A)
   \[3\pi \,c{{m}^{2}}\]                       done clear
  B)
   \[6\pi \,c{{m}^{2}}\]           done clear
  C)
   \[9\pi \,c{{m}^{2}}\]                       done clear
  D)
          \[7\pi \,c{{m}^{2}}\] done clear
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• question_answer14)
  The ratio of the outer and inner perimeters of a circular path is\[23:22\]. If the path is 5 metres wide, the diameter of the inner circle is
  A)
   \[55\,m\]                                  done clear
  B)
   \[110\,m\]                    done clear
  C)
  \[220\text{ }m\]         done clear
  D)
          \[~230\text{ }m\]       done clear
  View Solution play_arrow

• question_answer15)
  In the given figure, a semicircle is drawn with O as centre and AB as diameter. Semicircles are drawn with AO and OB as diameters. If \[AB=28\text{ }m,\]find the perimeter of the shaded region. \[\left[ Use\,\,\pi =\frac{22}{7} \right]\]                        
  A)
   \[70\text{ }m\]            done clear
  B)
   \[105\text{ }m\]          done clear
  C)
   \[88\text{ }m\]          done clear
  D)
          \[85\text{ }m\] done clear
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• question_answer16)
  An oval shaped meeting table made of wood has its dimensions as shown in figure. Find the cost of polishing it at \[Rs.\text{ }3.50\]per sq. m. (Use\[\pi =3.14\])                        
  A)
   \[Rs.\,310.75\]             done clear
  B)
   \[Rs.\,308.91\]       done clear
  C)
          \[Rs.\,250.25\]       done clear
  D)
         \[Rs.\,360.82\]          done clear
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• question_answer17)
  The diameter of the driving wheel of a bus is 140 cm. How many revolutions per minute must the wheel make in order to keep a speed of 66 km per hour?
  A)
   200                 done clear
  B)
   210                 done clear
  C)
   250                 done clear
  D)
   240  done clear
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• question_answer18)
  A square water tank has its sides equal to 40 m. There are four semicircular grassy plots all round it. Find the cost of turfing the plots at \[Rs.\text{ }1.25\]per sq. m.           
  A)
   Rs.2671         done clear
  B)
   Rs.4401                      done clear
  C)
   Rs.2512         done clear
  D)
          Rs.3140 done clear
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• question_answer19)
  A man runs around a circle of radius 50 m at a speed of 12 km/h. The time taken by him for going around it ten times is ___. \[(\pi =3.14)\]
  A)
   10 mins 42 sees done clear
  B)
   12 mins 35 sees done clear
  C)
   15 mins 42 sees done clear
  D)
   10 mins 35 sees done clear
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• question_answer20)
  A rectangular park is 100 m by 50 m. It is surrounded by semicircular flower beds all round. Find the cost of levelling the semicircular flower beds at 60 paise per\[{{m}^{2}}\].
  A)
   Rs.31425                    done clear
  B)
   Rs. 28260                   done clear
  C)
   Rs.352.40       done clear
  D)
          Rs. 282.60 done clear
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• question_answer21)
  In the given figure three circles of radius 2 cm touch one another externally. These circles are circumscribed by a circle of radius R cm. Find the value of R and the area of the shaded region in terms of \[\pi \]and \[\sqrt{3}\].
  A)
   \[\left\{ \frac{5\pi }{3}(5\sqrt{3}+1)-5\sqrt{3} \right\}\]             done clear
  B)
   \[\left\{ \frac{4\pi }{2}(4\sqrt{2}+1)-4\sqrt{2} \right\}\] done clear
  C)
   \[\left\{ \frac{4\pi }{3}(4\sqrt{3}+1)-4\sqrt{2} \right\}\] done clear
  D)
            \[\left\{ \frac{4\pi }{3}(4\sqrt{3}+1)-4\sqrt{3} \right\}\] done clear
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• question_answer22)
  Match the shaded region given in Column-l with their areas in Column-ll.                    

  Column-l	Column-II
  (P)	(i)  \[262.50\text{ }c{{m}^{2}}\]
  (Q)	(ii)  \[271.04\text{ }c{{m}^{2}}\]
  (R)	(iii)  \[427.14\,\,c{{m}^{2}}\]

             
  A)
   (P) \[\to \](iii); (Q) \[\to \](ii);   (R) \[\to \] (i)       done clear
  B)
   (P) \[\to \] (ii); (Q) \[\to \] (i);   (R)\[\to \] (iii)       done clear
  C)
   (P) \[\to \] (ii); (Q) \[\to \] (iii);             (R) \[\to \] (i)       done clear
  D)
   (P) \[\to \] (iii); (Q) \[\to \](i);   (R) \[\to \] (ii)       done clear
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• question_answer23)
  The circumcircle of \[\Delta ABC\] with \[\angle A={{60}^{o}}\]has its centre at O and radius equal to 2 cm. Circle centered at O., touches the circumcircle and also 08 and OC. The radius of the smaller circle is (in cm)____.
  A)
   \[12-4\sqrt{3}\]           done clear
  B)
   \[\frac{6-\sqrt{3}}{2}\]          done clear
  C)
   \[\frac{3-\sqrt{3}}{2}\]        done clear
  D)
   \[4\sqrt{3}-6\]             done clear
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• question_answer24)
  In the given figure, ABC is a right-angled triangle, right-angled at/A. Semicircles are drawn on AB, AC and BC as diameters. Find the area of the shaded region.
  A)
   7 sq. units                   done clear
  B)
   8 sq. units                   done clear
  C)
   5 sq. units       done clear
  D)
          6 sq. units done clear
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• question_answer25)
  In the given figure, ABCD is a square of side 10 cm. Find

  (i) Area of inscribed circle

  (ii) Area of circumscribed circle

  (iii) Area of shaded region

  A)

  	(i)	(ii)	(iii)
  	\[\frac{1100}{7}c{{m}^{2}}\]	\[\frac{550}{7}c{{m}^{2}}\]	\[\frac{550}{7}c{{m}^{2}}\]

                  done clear
  B)

  	(i)	(ii)	(iii)
  	\[\frac{550}{7}c{{m}^{2}}\]	\[\frac{1100}{7}c{{m}^{2}}\]	\[\frac{550}{7}c{{m}^{2}}\]

                  done clear
  C)

  	(i)	(ii)	(iii)
  	\[\frac{550}{7}c{{m}^{2}}\]	\[\frac{550}{7}c{{m}^{2}}\]	\[\frac{1100}{7}c{{m}^{2}}\]

                  done clear
  D)

  	(i)	(ii)	(iii)
  	\[\frac{1100}{7}c{{m}^{2}}\]	\[\frac{1100}{7}c{{m}^{2}}\]	\[\frac{550}{7}c{{m}^{2}}\]

  done clear
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