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Uttarakhand Board Class 10 Areas Related to Circles — practice questions

Explore 36 free Areas Related to Circles questions in Uttarakhand Board Class 10 Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Areas Related to Circles questions and exercises with answers

Showing questions 1–30 of 36.

The formula for the area of a sector of a circle of radius r and angle theta (in degrees) isRead the answer and worked solution →The formula for the length of an arc of a circle of radius r and angle theta (in degrees) isRead the answer and worked solution →A sector with central angle 90 degrees in a circle of radius 14 cm has areaRead the answer and worked solution →A circle has radius 7 cm. The area of a semicircle isRead the answer and worked solution →A segment of a circle is the region bounded by a chord and the correspondingRead the answer and worked solution →The area of a quadrant of a circle of radius r isRead the answer and worked solution →The area of a sector of a circle of radius 14 cm with central angle 60 degrees isRead the answer and worked solution →The length of the minute hand of a clock is 14 cm. The area swept by the minute hand in 5 minutes isRead the answer and worked solution →The arc length of a sector with radius 21 cm and angle 60 degrees isRead the answer and worked solution →A circular park of radius 20 m is to be enclosed by fencing. The length of fencing needed isRead the answer and worked solution →The area of a sector subtending 45 degrees at the centre of a circle of radius 8 cm isRead the answer and worked solution →A horse is tethered to a corner of a square field of side 15 m by a 7 m rope. The area the horse can graze isRead the answer and worked solution →A circular pizza of radius 14 cm is cut into 6 equal sectors. The area of each sector isRead the answer and worked solution →A wire is bent in the form of a circle of radius 28 cm. The same wire is then re-bent in the form of a square. The side of the square isRead the answer and worked solution →The area swept by the hour hand of length 5 cm in 4 hours isRead the answer and worked solution →A chord of a circle of radius 12 cm subtends an angle of 60 degrees at the centre. The area of the corresponding minor segment is approximatelyRead the answer and worked solution →The perimeter of a sector of a circle of radius 14 cm and angle 90 degrees isRead the answer and worked solution →The radius of a wheel is 21 cm. The number of revolutions to cover 924 m isRead the answer and worked solution →A circular flower bed has area 49 pi sq m. Its diameter isRead the answer and worked solution →A circle of radius 21 cm has a sector of angle 120 degrees. The area of the corresponding major segment is approximatelyRead the answer and worked solution →The area swept by the minute hand of length 14 cm in 35 minutes isRead the answer and worked solution →A square is inscribed in a circle of radius r. The area between the circle and the square isRead the answer and worked solution →Two circles of radius 7 cm overlap so that each passes through the other centre. The area of the lens-shaped overlap region (where pi=22/7) is approximatelyRead the answer and worked solution →A circle is inscribed in an equilateral triangle of side 12 cm. The area of the region between the triangle and the circle is approximatelyRead the answer and worked solution →A wire bent into a circle of radius 42 cm is now bent into a regular hexagon. The side of the hexagon isRead the answer and worked solution →The diameter of a wheel is 70 cm. The number of revolutions to go 11 km isRead the answer and worked solution →A circular field of radius 56 m has a path of width 7 m running around it. The area of the path isRead the answer and worked solution →Two concentric circles have areas in the ratio 1 : 4. The ratio of their radii isRead the answer and worked solution →A square is circumscribed about a circle of radius 7 cm. The area enclosed between the circle and the square isRead the answer and worked solution →A wheel of diameter 84 cm makes 75 revolutions. The distance covered isRead the answer and worked solution →

Worked practice questions

The formula for the area of a sector of a circle of radius r and angle theta (in degrees) is

  1. (theta/360) × pi × r squared
  2. (theta/180) × pi × r
  3. pi × r × theta
  4. (theta/360) × 2 × pi × r
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Correct answer: A. (theta/360) × pi × r squared

1. A full circle (360 degrees) has area pi × r squared. 2. A sector of angle theta is the fraction theta/360 of that. 3. Hence area = (theta/360) × pi × r squared. _Source: syllabus Mathematics, Ch 11 "Areas Related to Circles", §11.2_

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The formula for the length of an arc of a circle of radius r and angle theta (in degrees) is

  1. (theta/180) × pi × r squared
  2. (theta/360) × 2 × pi × r
  3. pi × r squared
  4. 2 × pi × r
Show answer and solution

Correct answer: B. (theta/360) × 2 × pi × r

1. A full circle (360 degrees) has circumference 2 × pi × r. 2. An arc of angle theta is the fraction theta/360 of that. 3. Hence arc length = (theta/360) × 2 × pi × r. _Source: syllabus Mathematics, Ch 11 "Areas Related to Circles", §11.2_

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A sector with central angle 90 degrees in a circle of radius 14 cm has area

  1. 49 sq cm
  2. 77 sq cm
  3. 154 sq cm
  4. 38.5 sq cm
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Correct answer: C. 154 sq cm

1. Area = (90/360) × (22/7) × 14 × 14. 2. = (1/4) × (22/7) × 196 = (1/4) × 616 = 154 sq cm. 3. Hence 154 sq cm. _Source: syllabus Mathematics, Ch 11 "Areas Related to Circles", §11.2_

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