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Circles Practice Questions: Level 01

Solve the given practice questions based on circles. Also, the answer key and explanations are given for the same.
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  1. What is the radius of a circle if its perimeter is numerically equal to thrice its area?
    A. 2
    B. 3
    C. 2/3
    D. 4

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    Answer : Option C
    2πr = 3πr2
    ⇒ r = 2/3
  2. The area of the sector of a circle, whose radius is 12 metres when the angle at the centre is 60, is
    A. 13.2 m2
    B. 75.42 m2
    C. 13.4 m2
    D. None of these
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    Answer : Option A
    Area of the sector r = πr2θ/360. θ = 60°, and radius = 12m So area = (22/7) × (12×12×60 / 360) ⇒ = 75.42m2
  3. Find the radius of the circle if area of sector is 924cm2 and angle at the center is 60.
    A. 42
    B. 21
    C. 22
    D. 46

    Answer : Option A
    A= πr2 × 60/360 = 924
    &⇒ r =42
  4. The difference between the circumference and area of a circle is 110 metres. Find its circumference.
    A. 44m
    B. 84m
    C. 30m
    D. 7m

    Answer : Option A
    πr2 - 2Πr = 110
    ⇒ r= 7
    Circumference = 2×22/7×7 = 44
  5. When the radius of a circle is decreased by 100%, the area of the circle:
    A. decreases by 50%
    B. decreases by 100%
    C. increases by 100%
    D. decreases by 200%

    Answer : Option B
    Since the radius of circle is reduced by 100%, the radius becomes 0.
    Therefore, area also decreases to 0.
    So, the area of the circle decreases by 100%.
Must Read Circle Articles
  1. Find circumference of a circle if area of the circle is 154 cm2.
    A. 18
    B. 22
    C. 44
    D. 66

    Answer : Option A
    22/7 ×r2 = 154 r = 7 Circumference = 2×22/7×7 =44 cm
  2. The difference between the circumference and the diameter of the circle is 60 cm. The area of the circle is:
    A. 425 cm2
    B. 616
    C. 154cm2
    D. 308 cm2

    Answer : Option B
    πD-D=60
    D=60/(π-1)=60/(15/7)=28
    Now area = π/4 × D2 = 616cm2
  3. The circle is 21 cm and m (arc RYS) = 60°. Find the area of the sector.
    A. 38.5 cm2
    B. 231 cm2
    C. 25.66 cm2
    D. 6.42 cm2

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    Answer : Option B
    Area of circle = π × 21×21×60/360 = 231cm2
  4. A regular hexagon is inscribed in a circle of radius 10 cm. Find the area of the shaded portion. (× ≈ 3.14 ; √3 ≈ 1.73).
    A. 271 cm2
    B. 54.5 cm2
    C. 290 cm2
    D. 75 cm2

    Answer : Option B
    Area of circle = π × 102 = 3.14 × 100 = 314 cm2.
    Area of regular hexagon = 6 × √3 / 4 × 10 × 10 = 259.5cm2.
    Area of shaded region = area of circle – area of hexagon = 314 – 259.5 = 54.5cm2. .
  5. The radius of a circle is decreased by 40%. What will be the percentage decrease in its surface area?
    A. 64%
    B. 36%
    C. 20%
    D. 10%

    Answer : Option A
    New area = 0.6 × 0.6 of the initial area= 0.36 of the initial area.
    So, 64% decrease.
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