CBSE Class 10 Mathematics Areas related to circles MCQs Set 03

Question. What is the area of the largest triangle that can be inscribed in a semicircle whose radius is ‘r’ cm?
(a) 2r cm²
(b) r² cm²
(c) 2r² cm²
(d) r/2 cm²

Answer: B

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 cm²
(b) 65 cm²
(c) 52 cm²
(d) 45 cm²

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: π
(b) π : 2
(c) π : 4
(d) 4 : π

Answer: A

Question. 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 π = 3.14 .)

Find the total area that Arjun shaded.
(a) 25.12 cm²
(b) 29.25 cm²
(c) 36.4 cm²
(d) 45.2 cm²

Answer: A

Question. A copper wire, when bent in the form of a square, encloses an area of 484 cm² . If the same wire is bent in the form of a circle, find the area in cm2 .
(a) 606
(b) 661
(c) 616
(d) 610

Answer: C

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°
(b) 2.73°
(c) 2.37°
(d) 3.27°

Answer: B

Question. The given figure is made up of a rectangle and 2 identical circles. Given that the length of the rectangle is 28 cm.

What is the area of the shaded region? (Use π = 22/7).
(a) 119 cm²
(b) 105 cm²
(c) 152 cm²
(d) 123 cm²

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. The area of a quadrant of a circle whose circumference is 616 cm will be
(a) 7546 cm²
(b) 7500 cm²
(c) 7456 cm²
(d) 7564 cm²

Answer: A

Question. The given figure shows 2 identical circles inside a rectangle in 2 cm .

Find the shaded area of the figure. (Take π = 3.14.)
(a) 1300
(b) 1154
(c) 1092
(d) 1256

Answer: D

Question. The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm is
(a) 31 cm
(b) 25 cm
(c) 62 cm
(d) 50 cm

Answer: D

Question. The diameter of a wheel is 1 m. The number of revolutions it will make to travel a distance of 22 km will be
(a) 2,800
(b) 4,000
(c) 5,500
(d) 7,000

Answer: D

Question. 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 π = 22/7.)

If the shaded region is covered with grass, find the area of the land covered with grass.
(a) 502 m²
(b) 497 m²
(c) 433 m²
(d) 564 m²

Answer: B

Question. A circular park has a path of uniform width around it. The difference between the outer and inner circumferences of the circular park is 132 cm. Its width is
(a) 20 cm
(b) 21 cm
(c) 22 cm
(d) 24 cm

Answer: B

Question. The ratio of the areas of a circle and an equilateral triangle whose diameter and a side are respectively equal is
(a) π : √2
(b) π : √3
(c) √3 : π
(d) √2 : π

Answer: B

Question. The figure given shows a rectangle with a semi-circle and 2 identical quadrants inside it. What is the shaded area of the figure? (Use π = 22/6 7 )

(a) 363 cm²
(b) 259 cm²
(c) 305 cm²
(d) 216 cm²

Answer: B

Question. The area of a square inscribed in a circle of diameter p cm is
(a) p² cm²
(b) p/4cm²
(c) p ² /2 cm²
(d) p /2 cm²

Answer: C

Question. If the ratio of the areas of the two circles is 25 : 16, then the ratio of their circumferences is
(a) 25/ 16
(b) 4/ 5
(c) 5 /4
(d) 500 /625

Answer: C

Question. If the sector of a circle of diameter 14cm subtends an angleof 30° at the centre, then its area is
(a) 49π
(b) 49π/12
(c) 242/ 3π
(d) 121/ π

Answer: B

Question. 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 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 π = 3.14 .)
(a) 449.75 cm²
(b) 520.60 cm²
(c) 563.72 cm²
(d) 450.92 cm²

Answer: D

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. 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. 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 cm²
(b) 241.8 cm²
(c) 79.27 cm²
(d) 173.9 cm²

Answer: A

Question. The figure shows a right-angled triangle and a semicircle. PQ is the diameter of the semicircle.

Find the perimeter of the whole figure.
(a) 13 + 8π
(b) 30 + 5π
(c) 18 + 6π
(d) 18 + 10π

Answer: C

Question. If the sector of a circle of diameter 10 cm subtends an angle of 144° at the centre, then the length of the arc of the sector is
(a) 2π cm
(b) 4π cm
(c) 5π cm
(d) 6π cm

Answer: B

Question. If the radius of a circle is diminished by 10%, then its area is diminished by
(a) 10%
(b) 19%
(c) 36%
(d) 20%

Answer: B

Question. The area of a circular ring formed by two concentric circles whose radii are 5.7 cm and 4.3 cm respectively is (Take π = 3.1416)
(a) 43.98 sq.cm
(b) 53.67 sq. cm
(c) 47.24 sq.cm
(d) 38.54 sq.cm

Answer: A

Question. A sector is cut from a circular sheet of radius 100 cm, the angle of the sector being 240º. If another circle of the area same as the sector is formed, then radius of the new circle is
(a) 79.5 cm
(b) 81.6 cm
(c) 83.4 cm
(d) 88.5 cm

Answer: B

Question. Which of the following is/are not correct?
(a) Area of a circle with radius 6 cm, if angle of sector is 60°, is 132/14cm². 
(b) If a chord of circle of radius 14 cm makes an angleof 60° at the centre of the circle, then area of major  sector is 512.87 cm².
(c) The ratio between the circumference and area of a circle of radius 5 cm is 2 : 5.
(d) Area of a circle whose radius is 6 cm, when the length of the arc is 22 cm, is 66 cm².

Answer: A

Fill in the Blanks :

Question. The region enclosed by an arc and a chord is called the …………….. of the circle.
Answer: segment

Question. A sector of a circle is called a …………….. sector if the minor arc of the circle is a part of its boundary.
Answer: minor