CBSE Class 10 Mathematics Areas related to circles MCQs Set 07

Question. 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
Answer: D

Question. The radius of a circle is 14 m. Find the circumference of the circle.
(a) 616m
(b) 88m
(c) 154m
(d) 176m
Answer: B

Question. If the radius of a circle is \(\frac{7}{\sqrt{\pi}}\) cm, find the area of the circle.
(a) \(154 \text{ cm}^2\)
(b) \(\frac{49}{\pi} \text{ cm}^2\)
(c) \(22 \text{ cm}^2\)
(d) \(49 \text{ cm}^2\)
Answer: D

Question. 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
Answer: C

Question. If the circumference of a circle is 44 m, what is the area of the circle?
(a) \(6084.5 \text{ m}^2\)
(b) \(276.5 \text{ m}^2\)
(c) \(154 \text{ m}^2\)
(d) \(44 \text{ m}^2\)
Answer: C

Question. 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) \(1496 \text{ m}^2\)
(b) \(1450 \text{ m}^2\)
(c) \(1576 \text{ m}^2\)
(d) \(1694 \text{ m}^2\)
Answer: D

Question. How many plants will be there in a circular bed whose outer edge measures 30 cm allowing \(4 \text{ cm}^2\) for each plant?
(a) 18
(b) 750
(c) 24
(d) 120
Answer: A

Question. The difference between circumference and radius of a circle is 37 m. Find the circumference of the circle.
(a) 7 m
(b) 44 m
(c) 154 m
(d) 186 m
Answer: B

Question. 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
Answer: C

Question. 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
Answer: B

Question. 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) \(\frac{A}{C} = r\)
Answer: A

Question. Find the area of the sector of a circle, whose radius is 6 m when the angle at the centre is \(42^\circ\).
(a) \(13.2 \text{ m}^2\)
(b) \(14.2 \text{ m}^2\)
(c) \(13.4 \text{ m}^2\)
(d) \(14.4 \text{ m}^2\)
Answer: A

Question. 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) \(168 \text{ cm}^2\)
(b) \(148 \text{ cm}^2\)
(c) \(154 \text{ cm}^2\)
(d) \(176 \text{ cm}^2\)
Answer: B

Question. 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 \(60^\circ\).
(a) \(45.27 \text{ cm}^2\)
(b) \(40.27 \text{ cm}^2\)
(c) \(40.8 \text{ cm}^2\)
(d) \(44.27 \text{ cm}^2\)
Answer: B

Question. A sector of \(120^\circ\) 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
Answer: A

Question. 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) \(231 \text{ cm}^2\)
(b) \(221 \text{ cm}^2\)
(c) \(210 \text{ cm}^2\)
(d) \(200 \text{ cm}^2\)
Answer: A

Question. 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) 1890 m
(b) 1980 m
(c) 1900 m
(d) 1800 m
Answer: B

Question. 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) \(8\sqrt{3} \text{ cm}\)
(b) \(2\sqrt{3} \text{ cm}\)
(c) \(10\sqrt{3} \text{ cm}\)
(d) \(14\sqrt{3} \text{ cm}\)
Answer: C

Question. 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
Answer: D

Question. What is the area of the largest triangle that can be inscribed in a semicircle whose radius is 'r' cm?
(a) \(2r \text{ cm}^2\)
(b) \(r^2 \text{ cm}^2\)
(c) \(2r^2 \text{ cm}^2\)
(d) \(\frac{r^2}{2} \text{ cm}^2\)
Answer: B

Question. 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) \(\frac{\pi + 4x^2}{4}\) sq units
(b) \(\frac{(\pi + 4)x^2}{4}\) sq units
(c) \(\left(\frac{\pi + 8}{4}\right)x^2\) sq units
(d) \(2(\pi + 4)x^2\) sq units
Answer: C

Question. If a square of side 's' units is carved out from a circle, find the ratio of the areas of two figures.
(a) \(2 : \pi\)
(b) \(\pi : 2\)
(c) \(\pi : 4\)
(d) \(4 : \pi\)
Answer: A

Question. The outer diameter and the inner diameter of a circular path are 728m and 700 m respectively. Find the area of the circular path. (Use \(\pi = \frac{22}{7}\).)
(a) \(45260 \text{ m}^2\)
(b) \(25012 \text{ m}^2\)
(c) \(31416 \text{ m}^2\)
(d) \(19541 \text{ m}^2\)
Answer: C

Question. 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%
Answer: C

Question. 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
Answer: A

Question. 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
Answer: D

Question. A regular hexagon is inscribed in a circle of radius 14 cm. Find the area of the circle falling outside the hexagon.
(a) \(106.79 \text{ cm}^2\)
(b) \(241.8 \text{ cm}^2\)
(c) \(79.27 \text{ cm}^2\)
(d) \(173.9 \text{ cm}^2\)
Answer: A

Question. The figure given is made up of a circle and 3 identical semicircles. O 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
Answer: C

Question. 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) \(59 \text{ cm}^2\)
(b) \(65 \text{ cm}^2\)
(c) \(52 \text{ cm}^2\)
(d) \(45 \text{ cm}^2\)
Answer: C

Question. A square shaped bus shelter is supported on four circular poles. The 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) \(\left(x^2 - \frac{y^2}{\pi}\right) \text{ m}^2\)
(b) \(\left(y^2 + \frac{x^2}{\pi}\right) \text{ m}^2\)
(c) \(\left(x^2 + \frac{y^2}{\pi}\right) \text{ m}^2\)
(d) \(\left(y^2 - \frac{x^2}{\pi}\right) \text{ m}^2\)
Answer: D

Question. 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
Answer: A

Question. A copper wire, when bent in the form of a square, encloses an area of \(484 \text{ cm}^2\). If the same wire is bent in the form of a circle, find the area in \(\text{cm}^2\).
(a) 606
(b) 661
(c) 616
(d) 610
Answer: C

Question. 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 \(\text{cm}^2\).
(a) 20
(b) 24
(c) 42
(d) 40
Answer: C

Question. If the length of the arc of a circle having a central angle \(36^\circ\) is 22 cm, what is the area of the circle?
(a) \(3580 \text{ cm}^2\)
(b) \(3850 \text{ cm}^2\)
(c) \(3058 \text{ cm}^2\)
(d) \(3805 \text{ cm}^2\)
Answer: B

Question. 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) \(3.72^\circ\)
(b) \(2.73^\circ\)
(c) \(2.37^\circ\)
(d) \(3.27^\circ\)
Answer: B