NCERT Solutions for Class 10 Maths Chapter 12 - Areas Related to Circles

Q. The radii of two circles are 19 cm and 9 cm respectively. Find the radius and the area of the circle which has its circumference equal to the sum of the circumference of the two circles.

  • Ans. 28 cm, 2464 cm2.

Q. A car has two wipers which do not overlap. Each wiper has a blade of length 25 cm sweeping through an angle of 115°. Find the total area cleaned in each sweep of the blades.

Ans. 1254.96 cm2.

Q. To warn ships about underwater rocks, a lighthouse spread a red-coloured light over a sector of 80° angle to a distance of 16.5 km. Find the area of the sea over which the ships are warned. [Use π = 3.14]

Ans. 189.97 km2.

Q. An umbrella has 8 ribs. Assuming the umbrella to be a flat circle of radius 45 cm, find the area between two consecutive ribs of the umbrella.

  • Ans. 795.53 cm2.

Q. A circular brooch is made of silver wire and consists of 5 diameters (35 mm each) forming of equal dimensions. Calculate the total length of silver wire required and the area of each sector that is formed.

  • Ans. 285 mm, 96.25 mm2.
Chapter 12 Areas Related to Circles in One Shot
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Q. In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find : (i) the length of the arc, (ii) area of the sector formed by the arc, (iii) area of the segment formed by the corresponding chord of the arc.

  • Ans. (i) 22 cm, (ii) 231 cm2, (iii) 40.04 cm2.

Q. A chord PQ of length 12 cm subtends an arc of 120° at the centre of a circle. Find the area of the minor segment cut off by the chord PQ.

  • Ans. 88.44 cm2.

Q. AB and CD respectively are the arcs of two concentric circles of radii 21 cm and 7 cm and centre O. If ∠AOB = 30°, find the area of the shaded region.

  • Ans. 102.67 cm2.

Q. What is the role of saliva in the digestion of food?

  • Ans. Saliva is secreted by salivary glands. It contains enzyme ptyalin which acts upon starch to convert them into maltose. This action of ptyalin upon starch occurs in mouth.

Q. Find the area of the shaded region in the given figure, where a circular arc of radius 6 cm has been drawn with the vertex O of an equilateral
triangle OAB of side 12 cm as centre.

  • Ans. 156.6 cm2.