LIWA

Areas Related to Circles

CBSE Class 10 · Maths · Chapter 11

Past board exam questions

CBSE 2027 sample paper · 1 mark

The diameter of a car wheel is 21 cm. The number of complete revolutions it will make in moving 66 km is:

  1. 104
  2. 105
  3. 106
  4. 107
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105

CBSE 2027 sample paper · 1 mark

The arc of a circle is of length 6π cm and the sector it bound has an area of 24π cm². The radius of the circle is:

  1. 4 cm
  2. 8 cm
  3. 16 cm
  4. 18 cm
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8 cm

CBSE 2027 sample paper · 2 marks

Find the area of a sector of a circle with diameter 28 cm, If the length of the corresponding arc is 22 cm.

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Radius = (28)/(2) = 14 cm. Area of sector = (1)/(2) × l × r = (1)/(2) × 22 × 14 = 154 cm².

CBSE 2027 sample paper · 4 marks

An Art and craft teacher prepared a fan which looked like the sector of a circle using ice-cream sticks and black sheet as described below: (The fan is a sector of a circle of radius 10 cm. The part near the centre, where the ice-cream sticks show, is a sector of radius 4 cm; the black sheet covers the rest of the sector, the region between radius 4 cm and radius 10 cm.) (i) The angle subtended at the centre of the sector is 60°. Find the area of one face of the fan. (1) (ii) With the given sector angle of 60° at the centre, find area of black sheet used in the fan. (1) (iii)(A) The boundary of the black sheet region on one face is to be covered by a designer tape. What length of tape is required? (2) OR (iii)(B) If 29.6 cm of designer tape is required to cover the boundary of the black sheet region on one face of the fan, then evaluate the central angle of the sector. (2)

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θ = 60°, r = 4 cm, R = 10 cm. (i) Area of one face of the fan = (θ)/(360)π R2 = (60)/(360) × (22)/(7) × 102 = (1100)/(21) ≈ 52.38 cm². (ii) Area of black sheet = (θ)/(360)π(R2 - r2) = (60)/(360) × (22)/(7) × (100 - 16) = 44 cm². (iii)(A) Boundary of the black sheet region = two straight edges + outer arc + inner arc = 2(10 - 4) + (60)/(360) × 2 × (22)/(7)(10 + 4) = 12 + (44)/(3) = (80)/(3) cm (≈ 26.67 cm). OR (iii)(B) $2(10 - 4) + \frac{\theta}{360} \times 2 \times \frac{22}{7}(10 + 4) = 29.6 \Rightarrow \frac{\theta}{360} \times 88 = 17.6 \Rightarrow \theta = \frac{17.6 \times …

CBSE 2026 board paper · 1 mark

An arc AB subtends an angle of 70° at the centre of the circle with radius 3 cm. Area of the sector OAB is :

  1. (11)/(3) cm²
  2. 11 cm²
  3. 6·5 cm²
  4. 5·5 cm²
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5·5 cm²

CBSE 2026 board paper · 1 mark

An arc AB subtends an angle of 56° at the centre of the circle of radius 4·5 cm. The length of the arc AB is : (Use π = (22)/(7))

  1. 22 cm
  2. 4·4 cm
  3. (44)/(5) cm
  4. 44 cm
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4·4 cm

CBSE 2026 board paper · 1 mark

The area of a semi-circular disc whose diameter is 'd', is

  1. π d2
  2. (π d2)/(2)
  3. (π d2)/(8)
  4. (π d2)/(4)
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(π d2)/(8)

CBSE 2026 sample paper · 1 mark

The Olympic rings are made by taking five congruent circles of radius 1cm each, intersecting in such a way that the chord formed by joining the point of intersection of two circles is also of length 1cm. In the picture of the rings, the dotted regions are the four lens-shaped regions where adjacent rings overlap (blue and yellow, yellow and black, black and green, green and red); each such region is bounded by the two arcs that meet at the ends of the common chord (for the blue and yellow rings, the chord AB). Total area of all the dotted regions (assuming the thickness of the rings to be negligible) is

  1. 4[(π)/(12) - (√(3))/(4)] cm²
  2. [(π)/(6) - (√(3))/(4)] cm²
  3. 4[(π)/(6) - (√(3))/(4)] cm²
  4. 8[(π)/(6) - (√(3))/(4)] cm²
Show answer
8[(π)/(6) - (√(3))/(4)] cm²