
question_answer1) When the circumference and area of a circle are numerically equal, find the numerical value of its diameter.
A) \[\frac{\pi }{2}\]
B) 8
C) \[2\pi \]
D) 4
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question_answer2) The radius of a circle is 14 m. Find the circumference of the circle.
A) 616m
B) 88m
C) 154m
D) 176m
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question_answer3) If the radius of a circle is \[\frac{7}{\sqrt{\pi }}cm\], find the area of the circle.
A) \[\text{154}\,\text{c}{{\text{m}}^{\text{2}}}\]
B) \[\frac{49}{\pi }c{{m}^{2}}\]
C) \[\text{22 c}{{\text{m}}^{\text{2}}}\]
D) \[\text{49 c}{{\text{m}}^{\text{2}}}\]
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question_answer4) If the circumference of a circle is \[\frac{30}{\pi }\],what is the diameter of the circle?
A) \[60\pi \]
B) \[\frac{15}{\pi }\]
C) \[\frac{30}{{{\pi }^{2}}}\]
D) \[30\]
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question_answer5) If the circumference of a circle is 44 m, what is the area of the circle?
A) \[\text{6}0\text{84}.\text{5 }{{\text{m}}^{\text{2}}}\]
B) \[\text{276}.\text{5 }{{\text{m}}^{\text{2}}}\]
C) \[\text{154}\,{{\text{m}}^{\text{2}}}\]
D) \[\text{44}\,{{\text{m}}^{\text{2}}}\]
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question_answer6) A circular grass lawn of 35 m radius, has a path 7 m wide running around it on the outside. Find the area of the path.
A) \[\text{1496}\,{{\text{m}}^{\text{2}}}\]
B) \[\text{145}0\,{{\text{m}}^{\text{2}}}\]
C) \[\text{1576}\,{{\text{m}}^{\text{2}}}\]
D) \[\text{1694}\,{{\text{m}}^{\text{2}}}\]
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question_answer7) How many plants will be there in a circular bed whose outer edge measures 30 cm allowing\[~\text{4 c}{{\text{m}}^{\text{2}}}\]for each plant?
A) 18
B) 750
C) 24
D) 120
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question_answer8) The difference between circumference and radius of a circle is 37 m. Find the circumference of the circle.
A) 7m
B) 44m
C) 154 m
D) 186m
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question_answer9) If the ratio of areas of two circles is 16:25, what is the respective ratio of their circumferences?
A) 25:16
B) 5:4
C) 4:5
D) 3:5
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question_answer10) If the ratio of circumference of two circles is 4:9, what is the ratio of their respective areas?
A) 9:4
B) 16:81
C) 4:9
D) 2:3
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question_answer11) If the area of a circle is A, radius is 'r' and circumference is C. which of the following relations is true?
A) \[rC=2A\]
B) \[\frac{C}{A}=\frac{r}{2}\]
C) \[AC=\frac{{{r}^{2}}}{4}\]
D) \[\frac{A}{r}=C\]
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question_answer12) Find the area of the sector of a circle, whose radius is 6 m when the angle at the centre is\[\text{42}{}^\circ \].
A) \[\text{13}.\text{2}\,{{\text{m}}^{\text{2}}}\]
B) \[\text{14}.\text{2}\,{{\text{m}}^{\text{2}}}\]
C) \[\text{13}.\text{4}\,{{\text{m}}^{\text{2}}}\]
D) \[\text{14}.\text{4}\,{{\text{m}}^{\text{2}}}\]
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question_answer13) What is The area of a sector of a circle of radius 16 cm cut off by an arc which is 18.5 cm long?
A) \[\text{168}\,\text{c}{{\text{m}}^{\text{2}}}\]
B) \[\text{148}\,\text{c}{{\text{m}}^{\text{2}}}\]
C) \[\text{154}\,\text{c}{{\text{m}}^{\text{2}}}\]
D) \[\text{176}\,\text{c}{{\text{m}}^{\text{2}}}\]
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question_answer14) Find the area of a segment of a circle of radius 21 cm if the angle made by the arc of the segment has a measure of\[~\text{6}0{}^\circ \].
A) \[\text{45}.\text{27 c}{{\text{m}}^{\text{2}}}\]
B) \[\text{4}0.\text{27 c}{{\text{m}}^{\text{2}}}\]
C) \[\text{4}0.\text{8 c}{{\text{m}}^{\text{2}}}\]
D) \[\text{44}.\text{27 c}{{\text{m}}^{\text{2}}}\]
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question_answer15) A sector of\[\text{12}0{}^\circ \]cut out from a circle has an area of\[9\frac{3}{7}\]. What is the radius of the circle?
A) 3cm
B) 2.5 cm
C) 3.5 cm
D) 3.6 cm
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question_answer16) The length of the minute hand of a wall clock is 21 cm long. What is the area swept by it in 10 minutes?
A) \[\text{231 c}{{\text{m}}^{\text{2}}}\]
B) \[~\text{221 c}{{\text{m}}^{\text{2}}}\]
C) \[\text{21}0\,\text{c}{{\text{m}}^{\text{3}}}\]
D) \[\text{2}00\,\text{c}{{\text{m}}^{\text{2}}}\]
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question_answer17) The diameters of the wheels of a car are each 63 cm. Find the distance travelled by the car when the wheels make 1000 revolutions.
A) 1890m
B) 1980m
C) 1900m
D) 1800m
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question_answer18) The radius of a circle is 20 cm. Three more concentric circles are drawn inside it in such a manner that it is divided into four parts of equal area. Find the radius of one of the three concentric circles.
A) \[8\sqrt{3}\,cm\]
B) \[2\sqrt{3}\,cm\]
C) \[10\sqrt{3}\,cm\]
D) \[14\sqrt{3}\,cm\]
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question_answer19) A wire bent in the form of a circle of radius 42 cm is cut and again bent in the form of a square. What is the ratio of the regions enclosed by the circle and the square?
A) 11 :12
B) 21 :33
C) 22:33
D) 14:11
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question_answer20) What is the area of the largest triangle that can be inscribed in a semicircle whose radius is 'r' cm?
A) \[\text{2r}\,\text{c}{{\text{m}}^{\text{2}}}\]
B) \[{{\text{r}}^{\text{2}}}\text{ c}{{\text{m}}^{\text{2}}}\]
C) \[\text{2}{{\text{r}}^{\text{2}}}\text{ c}{{\text{m}}^{\text{2}}}\]
D) \[\frac{r}{2}\text{c}{{\text{m}}^{\text{2}}}\]
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question_answer21) The top of a dining table is rectangular, 2x units long and x units wide, with two semicircles along the breadth. Find the area of the table.
A) \[\frac{\pi +4{{x}^{2}}}{4}sq.\,units\]
B) \[\frac{(\pi +4)}{4}{{x}^{2}}\,sq.\,units\]
C) \[\left( \frac{\pi +8}{4} \right){{x}^{2}}\,sq.\,units\]
D) \[2(\pi +4){{x}^{2}}\,sq.\,units\]
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question_answer22) If a square of side 's' units is carved out from a circle, find the ratio of the areas of two figures.
A) \[\text{2}:\pi \]
B) \[\pi :2\]
C) \[\pi :4\]
D) \[4:\pi \]
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question_answer23) The figure shows an isosceles triangle and a semicircle with centre O. Given that the radius of the semicircle is 2.8 cm, find the perimeter of the given figure.
A) 15.6cm
B) 18.8cm
C) 16.8cm
D) 20.4cm
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question_answer24) The given figure shows two identical circles and a rectangle. What is the unshaded area of the figure in \[\text{c}{{\text{m}}^{\text{2}}}\]? (Take\[\pi =\text{3}.\text{14}\].)
A) 40
B) 43
C) 25
D) 33
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question_answer25) By The shaded part of the given figure shows a running track in a stadium. Find the area of the track. (Take \[\pi =\frac{22}{7}\].)
A) \[\text{2}0\text{58}\,{{\text{m}}^{\text{2}}}\]
B) \[\text{1546}\,{{\text{m}}^{\text{2}}}\]
C) \[\text{3514}\,{{\text{m}}^{\text{2}}}\]
D) \[\text{1923}\,{{\text{m}}^{\text{2}}}\]
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question_answer26) The figure shows a rightangled triangle and a semicircle. PQ is the diameter of the semicircle. Find the perimeter of the whole figure.
A) \[13+8\pi \]
B) \[\text{3}0+5\pi \]
C) \[\text{18}+\text{6}\pi \]
D) \[\text{18}+\text{1}0\pi \]
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question_answer27) The outer diameter and the inner diameter of a circular path are 728m and 700 m respectively. Find the area of the 22 circular path. (Use\[\pi =\frac{22}{7}\].)
A) \[\text{4526}0\,{{\text{m}}^{\text{2}}}\]
B) \[\text{25}0\text{12}\,{{\text{m}}^{\text{2}}}\]
C) \[\text{31416}\,{{\text{m}}^{\text{2}}}\]
D) \[\text{19541 }{{\text{m}}^{\text{2}}}\]
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question_answer28) If the circumference of a circle is increased by 50%, by what percent will its area be increased?
A) 75%
B) 100%
C) 125%
D) 150%
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question_answer29) Each wheel of a car makes 5 revolutions per second. If the diameter of a wheel is 84 cm, find the speed of the car in km/h. (Give your answer correct to the nearest km.)
A) 48 km / h
B) 32 km / h
C) 41 km / h
D) 25 km / h
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question_answer30) The figure given shows two identical semicircles cut out from a piece of coloured paper. Find the area of the remaining piece of paper. (Use\[\pi =\frac{22}{7}\].)
A) \[\text{296}.\text{1 c}{{\text{m}}^{\text{2}}}\]
B) \[\text{265}.\text{4 c}{{\text{m}}^{\text{2}}}\]
C) \[\text{221}.\text{5}\,\text{c}{{\text{m}}^{\text{2}}}\]
D) \[\text{2}0\text{1}.\text{7}\,\text{c}{{\text{m}}^{\text{2}}}\]
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question_answer31) Mrs. Vidya bought a piece of cloth as shown in the figure. The portion of the cloth that is not coloured consists of 6 identical semicircles. Find the area of the coloured portion.
A) \[\text{144 c}{{\text{m}}^{\text{2}}}\]
B) \[\text{126 c}{{\text{m}}^{\text{2}}}\]
C) \[\text{195}\,\text{c}{{\text{m}}^{\text{2}}}\]
D) \[\text{243 c}{{\text{m}}^{\text{2}}}\]
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question_answer32) The given figure shows a plot of land, which is made up of 2 semicircles, a rectangle and an isosceles triangle. The diameter of the bigger semicircle is 7 m longer than that of the smaller semicircle. (Use\[\pi =\frac{22}{7}\].) If the shaded region is covered with grass, find the area of the land covered with grass.
A) \[\text{5}0\text{2 }{{\text{m}}^{\text{2}}}\]
B) \[\text{497 }{{\text{m}}^{\text{2}}}\]
C) \[\text{433 }{{\text{m}}^{\text{2}}}\]
D) \[\text{564 }{{\text{m}}^{\text{2}}}\]
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question_answer33) The figure given is made up of a rectangle, 2 identical semicircles and a quadrant. Find the unshaded area of the figure. (Use\[\pi =\frac{22}{7}\].)
A) \[\text{135}0\,\text{c}{{\text{m}}^{\text{2}}}\]
B) \[\text{1154}\,\text{c}{{\text{m}}^{\text{2}}}\]
C) \[\text{14}00\,\text{c}{{\text{m}}^{\text{2}}}\]
D) \[~\text{126}0\,\text{c}{{\text{m}}^{\text{2}}}\]
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question_answer34) In the given figure, a circle with centre B overlaps another circle with centre A and a square. The ratio of areas of P and Q is 5 :4 and the area of Q is\[\frac{1}{8}\]the area of circle B. The radii of circle A and circle B are 10 cm and 8 cm respectively. Find the area of the unshaded part of the figure. (Take\[\pi =\text{3}.\text{14}\].)
A) \[\text{449}.\text{75 c}{{\text{m}}^{\text{2}}}\]
B) \[\text{52}0.\text{6}0\text{ c}{{\text{m}}^{\text{2}}}\]
C) \[\text{563}.\text{72 c}{{\text{m}}^{\text{2}}}\]
D) \[\text{45}0.\text{92 c}{{\text{m}}^{\text{2}}}\]
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question_answer35) In the given figure, O is the centre of the circle whose diameter is 14 cm. Find the perimeter of the figure. (Use \[\pi =\frac{22}{7}\].)
A) 134cm
B) 124cm
C) 112cm
D) 160cm
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question_answer36) A bucket is pulled from a well by means of a rope which is wound round a wheel of diameter 77 cm. Given that the bucket ascends in 1 minute 28 seconds with a uniform speed of 1.1 m/s, find the number of complete revolutions that the wheel makes in raising the bucket. (Take\[\pi =\frac{22}{7}\].)
A) 10
B) 55
C) 25
D) 40
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question_answer37) David cut out the given figure during one of his art classes. The figure is made up of rectangles and quadrants. If David wanted to colour the figure red. Find the total area that he needs to colour. (Use\[\pi =3.14\])
A) \[\text{383}.\text{68 c}{{\text{m}}^{\text{2}}}\]
B) \[\text{197}.\text{59 c}{{\text{m}}^{\text{2}}}\]
C) \[\text{173}.\text{45 c}{{\text{m}}^{\text{2}}}\]
D) \[\text{242}.\text{52 c}{{\text{m}}^{\text{2}}}\]
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question_answer38) The figure given shows two identical semicircles inside a square. (Use\[\pi =\frac{22}{7}\].) What is the shaded area of the region?
A) \[\text{15}\,\text{c}{{\text{m}}^{\text{2}}}\]
B) \[\text{21 c}{{\text{m}}^{\text{2}}}\]
C) \[\text{16}\,\text{c}{{\text{m}}^{\text{2}}}\]
D) \[~\text{23}\,\text{c}{{\text{m}}^{\text{2}}}\]
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question_answer39) A regular hexagon is inscribed in a circle of radius 14 cm. Find the area of the circle falling outside the hexagon.
A) \[\text{1}0\text{6}.\text{79 c}{{\text{m}}^{\text{2}}}\]
B) \[\text{241}.\text{8 c}{{\text{m}}^{\text{2}}}\]
C) \[\text{79}.\text{27 c}{{\text{m}}^{\text{2}}}\]
D) \[\text{173}.\text{9 c}{{\text{m}}^{\text{2}}}\]
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question_answer40) Kill In the given figure, ABC is a rightangled triangle in which \[\angle \text{ABC}=\text{9}0{}^\circ \], AB = 6 cm and BC = 8 cm. 0 is the centre of the in circle. Find the area of shaded region. (Use\[\pi =\frac{22}{7}\].)
A) \[\text{12}.\text{56}\,\text{c}{{\text{m}}^{\text{2}}}\]
B) \[\text{11}.\text{42}\,\text{c}{{\text{m}}^{\text{2}}}\]
C) \[\text{13}.\text{65c}{{\text{m}}^{\text{2}}}\]
D) \[\text{1}0.\text{57}\,\text{c}{{\text{m}}^{\text{2}}}\]
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question_answer41) Arjun drew a figure as shown in figure, where a circle is divided into 18 equal parts. He then shaded some of the parts. (Take\[\pi =\text{3}.\text{14}\].) Find the total area that Arjun shaded.
A) \[\text{25}.\text{12 c}{{\text{m}}^{\text{2}}}\]
B) \[\text{29}.\text{25 c}{{\text{m}}^{\text{2}}}\]
C) \[\text{36}.\text{4 c}{{\text{m}}^{\text{2}}}\]
D) \[~\text{45}.\text{2 c}{{\text{m}}^{\text{2}}}\]
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question_answer42) In the adjoining figure, ABC is an equilateral triangle of side 14 cm. M is the centre of the circumcircle. Find the area of the shaded region.
A) \[\text{115}.\text{27 c}{{\text{m}}^{\text{2}}}\]
B) \[\text{96}.\text{63 c}{{\text{m}}^{\text{2}}}\]
C) \[\text{12}0.\text{46 c}{{\text{m}}^{\text{2}}}\]
D) \[\text{146}.\text{72 c}{{\text{m}}^{\text{2}}}\]
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question_answer43) 4 identical semicircles are drawn inside a big square as shown. Each side of the big square is 14cm long. Find the area of the shaded region. (Use\[\pi =\frac{22}{7}\].)
A) \[\text{125}\,\text{c}{{\text{m}}^{\text{2}}}\]
B) \[\text{112 c}{{\text{m}}^{\text{2}}}\]
C) \[\text{173}\,\text{c}{{\text{m}}^{\text{2}}}\]
D) \[\text{159 c}{{\text{m}}^{\text{2}}}\]
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question_answer44) The figure given is made up of a square with a circle inscribed in it. What is the area of the shaded region? (Take\[\pi =\text{3}.\text{14}\].)
A) \[\text{6}.\text{28 c}{{\text{m}}^{\text{2}}}\]
B) \[\text{1}.\text{42 c}{{\text{m}}^{\text{2}}}\]
C) \[\text{4}.\text{91 c}{{\text{m}}^{\text{2}}}\]
D) \[\text{7}.\text{36 c}{{\text{m}}^{\text{2}}}\]
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question_answer45) The figure given is made up of a circle and 3 identical semicircles. 0 is the centre of the circle and XY is the diameter of the circle. Given that XY is 28 cm, find the perimeter of the shaded part of the figure. (Use \[\pi =\frac{22}{7}\].)
A) 67 cm
B) 50 cm
C) 80 cm
D) 15 cm
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question_answer46) The figure given shows a rectangle with a semicircle and 2 identical quadrants inside it. What is the shaded area of the figure? (Use\[\pi =\frac{22}{7}\].)
A) \[\text{363 c}{{\text{m}}^{\text{2}}}\]
B) \[\text{259 c}{{\text{m}}^{2}}\]
C) \[\text{3}0\text{5}\,\text{c}{{\text{m}}^{\text{2}}}\]
D) \[\text{216}\,\text{c}{{\text{m}}^{\text{2}}}\]
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question_answer47) The minute hand of a clock is 7 cm long. Find the area traced out by the minute hand of the clock between 4:15 p.m. and 4:35 p.m. on a day.
A) \[\text{59 c}{{\text{m}}^{\text{2}}}\]
B) \[\text{65 c}{{\text{m}}^{\text{2}}}\]
C) \[\text{52 c}{{\text{m}}^{\text{2}}}\]
D) \[~\text{45 c}{{\text{m}}^{\text{2}}}\]
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question_answer48) A square shaped bus shelter is supported on four circular polesThe circumference of each pole is '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) \[\left( {{x}^{2}}\frac{{{y}^{2}}}{p} \right){{m}^{2}}\]
B) \[\left( {{y}^{2}}+\frac{{{x}^{2}}}{p} \right){{m}^{2}}\]
C) \[\left( {{x}^{2}}+\frac{{{y}^{2}}}{p} \right){{m}^{2}}\]
D) \[\left( {{y}^{2}}\frac{{{x}^{2}}}{p} \right){{m}^{2}}\]
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question_answer49) The circumference of a circle exceeds its diameter by 30 cm. Find the radius of the circle.
A) 7 cm
B) 14 cm
C) 21 cm
D) 28 cm
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question_answer50) The given figure shows 2 identical circles inside a rectangle in\[\text{c}{{\text{m}}^{\text{2}}}\]. Find the shaded area of the figure. (Take\[\pi =\text{3}.\text{14}\].)
A) 1300
B) 1154
C) 1092
D) 1256
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question_answer51) A copper wire, when bent in the form of a square, encloses an area of\[\text{484 c}{{\text{m}}^{\text{2}}}\]. If the same wire is bent in the form of a circle, find the area in \[\text{c}{{\text{m}}^{\text{2}}}\].
A) 606
B) 661
C) 616
D) 610
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question_answer52) Four equal circles are described about the four corners of a square so that each of them touches two of the others. If each side of the square measures 14 cm, find the area of the remaining portion of the square apart from four circles in\[\text{c}{{\text{m}}^{\text{2}}}\].
A) 20
B) 24
C) 42
D) 40
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question_answer53) If the length of the arc of a circle having a central angle 36? is 22 cm, what is the area of the circle?
A) \[\text{358}0\text{ c}{{\text{m}}^{\text{2}}}\]
B) \[\text{385}0\text{ c}{{\text{m}}^{\text{2}}}\]
C) \[\text{3}0\text{58 c}{{\text{m}}^{\text{2}}}\]
D) \[~\text{38}0\text{5 c}{{\text{m}}^{\text{2}}}\]
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question_answer54) If the perimeter of an arc of a circle is 43 cm and the radius of the circle is 21 cm, find the angle subtended at the centre.
A) \[\text{3}.\text{72}{}^\circ \]
B) \[\text{2}.\text{73}{}^\circ \]
C) \[\text{2}.\text{37}{}^\circ \]
D) \[\text{3}.\text{27}{}^\circ \]
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question_answer55) The given figure is made up of a rectangle and 2 identical circles. Given that the length of the rectangle is 28 cm.
A) \[\text{119 c}{{\text{m}}^{\text{2}}}\]
B) \[\text{1}0\text{5 c}{{\text{m}}^{\text{2}}}\]
C) \[\text{152}\,\text{c}{{\text{m}}^{\text{2}}}\]
D) \[\text{123 c}{{\text{m}}^{\text{2}}}\]
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