10th Class Mathematics Areas Related to Circles Question Bank

done Area of Circle Total Questions - 40

• question_answer1)
  If the area of circle inscribed in an equilateral triangle is \[48\pi \] square units then what is the perimeter of that triangle?
  A)
   \[17\sqrt{3}\] units                     done clear
  B)
   \[36\]units          done clear
  C)
   \[72\]units          done clear
  D)
   \[48\sqrt{3}\] units done clear
  View Solution play_arrow

• question_answer2)
  If the perimeter of a semi-circular protractor is 36 cm, what is its diameter?
  A)
   11 cm                          done clear
  B)
   13 cm          done clear
  C)
   15 cm                          done clear
  D)
   14 cm done clear
  View Solution play_arrow

• question_answer3)
  In the given figure, two circles of radii 7 cm each are shown. ABCD is a rectangle and AD and BC are the radii. What is the area of shaded region?
  A)
   \[20\text{ }c{{m}^{2}}\]                     done clear
  B)
   \[21\text{ }c{{m}^{2}}\]     done clear
  C)
   \[19\text{ }c{{m}^{2}}\]                     done clear
  D)
   \[18\text{ }c{{m}^{2}}\] done clear
  View Solution play_arrow

• question_answer4)
  A race track is in the form of a circular ring that has inner and outer circumferences are 500 m and 599 m respectively. What is the width of the track?
  A)
   11 m                            done clear
  B)
   22 m            done clear
  C)
   15.75 m  done clear
  D)
   10.75 m done clear
  View Solution play_arrow

• question_answer5)
  What is the Perimeter of the shaded region?
  A)
   264 cm done clear
  B)
   352 cm         done clear
  C)
   500 cm                         done clear
  D)
   528 cm done clear
  View Solution play_arrow

• question_answer6)
  The minute hand of a wall clock is of length 10.5 cm. What is the area covered by it in 60 minutes?
  A)
   \[346.5\text{ }c{{m}^{2}}\]     done clear
  B)
   \[340\text{ }c{{m}^{2}}\]         done clear
  C)
   \[355\text{ }c{{m}^{2}}\]                   done clear
  D)
   \[342\text{ }c{{m}^{2}}\] done clear
  View Solution play_arrow

• question_answer7)
  Four horses are tethered at four corners of a square plot of 42 m so that they just cannot reach one another. The area left ungrazed is:
  A)
   \[378\,{{m}^{2}}\]   done clear
  B)
   \[438\,{{m}^{2}}\]          done clear
  C)
   \[786\,{{m}^{2}}\]                  done clear
  D)
   None of these done clear
  View Solution play_arrow

• question_answer8)
  The diagram shows two concentric circles. The chord of the large circle is a tangent to the small circle and has length 2k. What is the area of the shaded region?
  A)
   \[\pi {{k}^{2}}\]          done clear
  B)
   \[3\pi {{k}^{2}}\]             done clear
  C)
   \[5\pi {{k}^{2}}\]                    done clear
  D)
   \[2\pi {{k}^{2}}\] done clear
  View Solution play_arrow

• question_answer9)
  If the circumferences of a circle is increased by 50%, by what percent will its area be increased?
  A)
   75%                             done clear
  B)
   100%          done clear
  C)
   125%    done clear
  D)
   150% done clear
  View Solution play_arrow

• question_answer10)
  Figure ABCD is a square with side 10 cm. BMD is an arc of a circle with centre C. BND is an arc of a circle with centre A. What is the area of the shaded region?
  A)
   \[\left( 100-25\pi  \right)\text{ }c{{m}^{2}}\]      done clear
  B)
   \[\left( 100-50\pi  \right)c{{m}^{2}}\] done clear
  C)
   \[\left( 50\pi -100 \right)c{{m}^{2}}\] done clear
  D)
   \[\left( 25\pi -100 \right)\text{ }c{{m}^{2}}\] done clear
  View Solution play_arrow

• question_answer11)
    An equilateral triangle has a circle inscribed in it and is circumscribed by a circle. There is another equilateral triangle inscribed in the inner circle. What is the ratio of the areas of the outer circle and the inner equilateral triangle?
  A)
   \[\frac{16\pi }{3\sqrt{3}}\] done clear
  B)
   \[\frac{8\pi }{2\sqrt{3}}\] done clear
  C)
   \[\frac{24\pi }{3\sqrt{3}}\]                     done clear
  D)
   None of these done clear
  View Solution play_arrow

• question_answer12)
  The top of dining table is rectangular, 2k units long and k units wide, with two semicircles along the breadth. What is the area of table?
  A)
   \[\frac{\pi +4{{k}^{2}}}{4}\]              done clear
  B)
   \[\frac{(\pi +4)}{4}{{k}^{2}}\] done clear
  C)
   \[\left( \frac{\pi +8}{4} \right){{k}^{2}}\] done clear
  D)
   \[2(\pi +4){{k}^{2}}\] done clear
  View Solution play_arrow

• question_answer13)
  In the given figure, PQRS is a square of diagonal \[7\sqrt{2}\,cm\]. With P as the centre, the arc QMS is drawn. What is the area of the shaded region \[(in\,\,c{{m}^{2}})\]?
  A)
   \[\frac{49}{4}(\pi -2)\] done clear
  B)
   \[\frac{49}{4}(\pi -1)\] done clear
  C)
   \[\frac{49}{4}(\pi -3)\] done clear
  D)
   \[\frac{49}{2}(\pi -2)\] done clear
  View Solution play_arrow

• question_answer14)
  A circular garden of radius is 15 m is surrounded by a circular path of width 7 m. If the path is to be covered with tiles at a rate of Rs. 10 per\[{{m}^{2}}\], then what is the total cost of the work?
  A)
   Rs. 8410          done clear
  B)
   Rs. 7140          done clear
  C)
   Rs. 8140       done clear
  D)
   Rs. 7410 done clear
  View Solution play_arrow

• question_answer15)
  Find the area of the shaded region, given that the radius of each circle is equal to 5 cm.
  A)
   \[(400-100\pi )\] done clear
  B)
   \[(360-100\pi )\]     done clear
  C)
   \[(231-100\pi )\]             done clear
  D)
   \[(400-50\pi )\] done clear
  View Solution play_arrow

• question_answer16)
  What is area of the shaded figure below?
  A)
   \[\frac{\pi }{\sqrt{3}}{{a}^{2}}\]                     done clear
  B)
   \[\frac{\pi {{a}^{2}}}{16}\] done clear
  C)
   \[\frac{\left( \pi -\sqrt{2} \right)}{4}{{a}^{2}}\]              done clear
  D)
   \[\frac{2\sqrt{3}}{\pi }{{a}^{2}}\] done clear
  View Solution play_arrow

• question_answer17)
  A circle is inscribed is an equilateral triangle. If the in-radius is 21 cm, what is the area of the triangle?
  A)
   \[1100\sqrt{3}\,c{{m}^{2}}\]               done clear
  B)
   \[1323\sqrt{3}\,c{{m}^{2}}\]   done clear
  C)
   \[1369\sqrt{3}\,c{{m}^{2}}\]               done clear
  D)
   \[1442\sqrt{3}\,c{{m}^{2}}\] done clear
  View Solution play_arrow

• question_answer18)
  In the given figure ABC is an equilateral triangle and C as the centre of the circle. A and B lie on the circle. What is the area of the shaded region, if the diameter of the circle is 28 cm?
  A)
   \[\left( 102\frac{2}{3}-49\sqrt{3} \right)c{{m}^{2}}\]     done clear
  B)
   \[\left( 103\frac{2}{3}-4998\sqrt{3} \right)c{{m}^{2}}\] done clear
  C)
   \[\left( 109-38\sqrt{3} \right)cm\] done clear
  D)
   None of these done clear
  View Solution play_arrow

• question_answer19)
  A square shaped bus shelter is supported on four circular poles. The circumferences of each pole are 'x' m and the length of each side of the shelter is 'y' m. find the area of the unsupported part of the shelter.
  A)
   \[\left( {{x}^{2}}-\frac{{{y}^{2}}}{\pi } \right){{m}^{2}}\]   done clear
  B)
   \[\left( {{y}^{2}}+\frac{{{x}^{2}}}{\pi } \right){{m}^{2}}\] done clear
  C)
   \[\left( {{x}^{2}}+\frac{{{y}^{2}}}{\pi } \right){{m}^{2}}\]              done clear
  D)
   \[\left( {{y}^{2}}-\frac{{{x}^{2}}}{\pi } \right){{m}^{2}}\] done clear
  View Solution play_arrow

• question_answer20)

  Four identical semicircles are drawn inside a big square as shown in the figure. Each side of the big square is 14 cm long.

  What is the area of the shaded region? (Use \[\pi =\frac{22}{7}\] )
  A)
   \[125\text{ }c{{m}^{2}}\]                   done clear
  B)
   \[112\text{ }c{{m}^{2}}\]        done clear
  C)
   \[173\text{ }c{{m}^{2}}\]                   done clear
  D)
   \[159\text{ }c{{m}^{2}}\] done clear
  View Solution play_arrow

• question_answer21)

  The figure given is made up of a rectangle, identical semicircle(s) and quadrant (s).

  What is the area of the un-shaded portion? (Use \[\pi =\frac{22}{7}\])
  A)
   \[1350\text{ }c{{m}^{2}}\]                  done clear
  B)
   \[1154\text{ }c{{m}^{2}}\]        done clear
  C)
   \[1400\text{ }c{{m}^{2}}\]                  done clear
  D)
   \[{{21}^{2}}\times \left( 6-\pi  \right)\text{ }c{{m}^{2}}\] done clear
  View Solution play_arrow

• question_answer22)
  An ink pen, with a cylindrical barrel of diameter 2 cm and height 10.5 cm, completely filled with ink, can be used to write 4950 words. How many words can be written using 400 ml of ink?
  A)
   40000              done clear
  B)
   60000     done clear
  C)
   450000             done clear
  D)
   80000 done clear
  View Solution play_arrow

• question_answer23)
  What is the area of the sector of a circle, whose radius is 6 m and the angle at the centre is\[42{}^\circ \]?
  A)
   \[13.2\text{ }{{m}^{2}}\]   done clear
  B)
   \[14.2\text{ }{{m}^{2}}\]           done clear
  C)
   \[13.4\text{ }{{m}^{2}}\]                    done clear
  D)
   \[14.4\text{ }{{m}^{2}}\] done clear
  View Solution play_arrow

• question_answer24)
  In the given figure, ABCD is a square of side 10 cm and a circle is inscribed in it. What is the area of the shaded part? (\[in\text{ }c{{m}^{2}}\])
  A)
   \[\frac{100-36\pi }{41}\]                        done clear
  B)
   \[\frac{100-25\pi }{8}\] done clear
  C)
   \[\frac{100+25\pi }{8}\]                        done clear
  D)
   None of these done clear
  View Solution play_arrow

• question_answer25)

  The given figure shows an isosceles triangle and a semicircle with centre O.

  If the radius of the semicircle is 2.8 cm. What is the perimeter of the figure?
  A)
   15.6 cm            done clear
  B)
   18.8 cm  done clear
  C)
   16.8 cm            done clear
  D)
   20.4 cm done clear
  View Solution play_arrow

• question_answer26)
  The given figure is made up of a circle and three identical semicircles. If O is the centre and XY is the diameter of the bigger circle respectively and XY is equal to 28 cm, What is the perimeter of the shaded part?
  A)
   67 cm                          done clear
  B)
   50 cm          done clear
  C)
   80 cm done clear
  D)
   15 cm done clear
  View Solution play_arrow

• question_answer27)
  The given figure shows two identical semicircles inside a square. What is the area of the shaded region?
  A)
   \[15\text{ }c{{m}^{2}}\]                                 done clear
  B)
   \[21\,c{{m}^{2}}\]        done clear
  C)
   \[16\,c{{m}^{2}}\]                              done clear
  D)
   \[23\,c{{m}^{2}}\] done clear
  View Solution play_arrow

• question_answer28)
  There is a circular road round a circular garden. If the difference between the circumferences of the outer circle and the inner circle is 44 m., what is the width of the road?
  A)
   5 m                              done clear
  B)
   6 m            done clear
  C)
   7 m         done clear
  D)
   8 m done clear
  View Solution play_arrow

• question_answer29)
  A circle of radius 'b' is divided into 6 equal sectors. An equilateral triangle is drawn on the chord of each sector to lie outside the circle. What is the area of the resulting figure?
  A)
   \[3{{b}^{2}}\left( \pi +\sqrt{3} \right)\]             done clear
  B)
   \[3\sqrt{3}{{b}^{2}}\] done clear
  C)
   \[3\left( {{b}^{2}}\sqrt{3}+\pi  \right)\]             done clear
  D)
   \[\frac{3\sqrt{3}\pi {{b}^{2}}}{2}\] done clear
  View Solution play_arrow

• question_answer30)
  What is the area of the given figure?
  A)
   \[115.5\text{ }c{{m}^{2}}\]   done clear
  B)
   \[228.5\text{ }c{{m}^{2}}\]        done clear
  C)
   \[154\text{ }c{{m}^{2}}\]                   done clear
  D)
   None of these done clear
  View Solution play_arrow

• question_answer31)
  A wire in the form of a circle of radius 42 cm is cut and again bent to form a square. What is the diagonal of the square?
  A)
   \[66\text{ }cm\]                         done clear
  B)
   \[66\sqrt{3}\,cm\]        done clear
  C)
   \[66\sqrt{2}\,cm\]          done clear
  D)
   None of these done clear
  View Solution play_arrow

• question_answer32)
  In the adjoining figure ACB is a quadrant with radius 'a'. A semicircle is drawn outside the quadrant taking AB as a diameter. What is the area of shaded region?
  A)
   \[\frac{1}{4}\left( \pi -2{{a}^{2}} \right)\]                      done clear
  B)
   \[\left( \frac{1}{4} \right)\left( \pi {{a}^{2}}-{{a}^{2}} \right)\] done clear
  C)
   \[\frac{{{a}^{2}}}{2}\]           done clear
  D)
   \[{{a}^{2}}\left( \frac{\pi -2}{2} \right)\] done clear
  View Solution play_arrow

• question_answer33)
  There are two circles intersecting each other. Another smaller circle with centre O is lying between the common regions of two larger circles. Centres of the circle (i.e., A, O and B) are lying on a straight line. If AB = 16 cm and the radii of the larger circles are 10 cm each, what is the area of the smaller circle?
  A)
   \[4\pi \text{ }c{{m}^{2}}\]    done clear
  B)
   \[2\pi \text{ }c{{m}^{2}}\]         done clear
  C)
   \[\frac{4}{\pi }\text{ }c{{m}^{2}}\]                 done clear
  D)
   \[\frac{\pi }{4}\text{ }c{{m}^{2}}\] done clear
  View Solution play_arrow

• question_answer34)
     ABCD is a squares, inside of it four circles with radius 1 cm. and touching each other are drawn. What is the area of the shaded region?
  A)
   \[(2\pi -3)c{{m}^{2}}\]                        done clear
  B)
   \[(4-\pi )c{{m}^{2}}\] done clear
  C)
   \[(16-4\pi )c{{m}^{2}}\]           done clear
  D)
   None of these done clear
  View Solution play_arrow

• question_answer35)
  Three circles of equal radii touch each other as shown in the figure. The radius of each circle is 1 cm. What is the area of the shaded region?
  A)
   \[\left( \frac{2\sqrt{3}-\pi }{2} \right)c{{m}^{2}}\]          done clear
  B)
   \[\left( \frac{3\sqrt{2}-\pi }{3} \right)c{{m}^{2}}\] done clear
  C)
   \[\frac{2\sqrt{3}}{\pi }c{{m}^{2}}\]                 done clear
  D)
   \[\frac{\sqrt{6}}{2\pi }c{{m}^{2}}\] done clear
  View Solution play_arrow

• question_answer36)
  A circular paper is folded along its diameter; then again it is folded to form a quadrant. Then it is cut as shown in the figure and after that the paper was reopened in the original circular shape. What is the ratio of the original paper to that of the remaining paper? (The shaded portion is cut off from the quadrant. The radius of quadrant OAB is 5 cm and radius of each semicircle is 1 cm):
  A)
   \[25:16\]        done clear
  B)
   \[25:9\]         done clear
  C)
   \[20:9\]                         done clear
  D)
   \[31:25\] done clear
  View Solution play_arrow

• question_answer37)
  ABCD is a square. A circle is inscribed in the square. Also taking A, B, C, D (the vertices of square) as the centers, four Quadrants are drawn, which are touching each other on the mid-point of the sides of square. If the Area of square is 4 cm 2, what is the area of the shaded region?
  A)
   \[\left( 4-\frac{3\pi }{2} \right)c{{m}^{2}}\]       done clear
  B)
   \[(2\pi -4)c{{m}^{2}}\] done clear
  C)
   \[(4-2\pi )c{{m}^{2}}\]            done clear
  D)
   \[\left( \frac{7-3\pi }{2} \right)c{{m}^{2}}\] done clear
  View Solution play_arrow

• question_answer38)
  In the adjoining diagram ABCD is a square with side 'a' cm. In the diagram the area of the larger circle with centre 'O' is equal to the sum of the areas of all the rest four circles with equal radii, whose centers are P, Q, R and S. What is the ratio between the diagonal of square and radius of a smaller circle?
  A)
   \[\left( 2\sqrt{2}+3 \right)\]                     done clear
  B)
   \[\left( 2+3\sqrt{2} \right)\] done clear
  C)
   \[\left( 4+3\sqrt{2} \right)\]                     done clear
  D)
   can't be determined done clear
  View Solution play_arrow

• question_answer39)
  In Fig, ABC is a right - angle triangle, \[\angle B=90{}^\circ ,AB=28\text{ }cm\] and \[BC=21\text{ }cm\]. With AC as diameter, a semicircle is drawn and with BC as radius, a quarter-circle is drawn. Find the area of the shaded region correct to two decimal places.
  A)
   \[428.75\,c{{m}^{2}}\]     done clear
  B)
   \[857.50\,c{{m}^{2}}\] done clear
  C)
   \[214.37\,c{{m}^{2}}\]                done clear
  D)
   \[371.56\,c{{m}^{2}}\] done clear
  View Solution play_arrow

• question_answer40)
    The area of the circle circumscribing three circles of unit radius touching each other is:
  A)
   \[(\pi /3){{\left( 2+\sqrt{3} \right)}^{2}}\] done clear
  B)
   \[6\pi {{\left( 2+\sqrt{3} \right)}^{2}}\] done clear
  C)
   \[3\pi {{\left( 2+\sqrt{3} \right)}^{2}}\]             done clear
  D)
   \[\left( \frac{\pi }{6} \right){{\left( 2+\sqrt{3} \right)}^{2}}\] done clear
  View Solution play_arrow