Mensuration


  1. The area of a sector of a circle of radius 5 cm, formed by an arc of length 3.5 cm is:









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    Using Rule 17,
    Here, l = arc length= 3.5 cm r = radius = 5 cm

    ∴ Area of sector =
    1
    lr
    2

    =
    1
    × 3.5 × 5 = 8.75 cm²
    2

    Correct Option: B

    Using Rule 17,
    Here, l = arc length= 3.5 cm r = radius = 5 cm

    ∴ Area of sector =
    1
    lr
    2

    =
    1
    × 3.5 × 5 = 8.75 cm²
    2


  1. The area (in sq. cm.) of the largest circle that can be drawn inside a square of side 28 cm,is :









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    The diameter of the largest circle inscribed inside a square is equal to its side.
    ∴ d = a = 28cm.

    Area of the circle =
    πd²
    4

    =
    1
    ×
    22
    × (28)² cm²
    47

    = 22 × 28 cm² = 616 cm²

    Correct Option: D


    The diameter of the largest circle inscribed inside a square is equal to its side.
    ∴ d = a = 28cm.

    Area of the circle =
    πd²
    4

    =
    1
    ×
    22
    × (28)² cm²
    47

    = 22 × 28 cm² = 616 cm²



  1. If the circumference of a circle increases from 4π to 8π, what change occurs in its area?









  1. View Hint View Answer Discuss in Forum

    When the circumference is doubled, it means radius of circle is doubled, as circumference
    = 2πr
    Since, area = πr², it will quadrupled.

    Correct Option: C

    When the circumference is doubled, it means radius of circle is doubled, as circumference
    = 2πr
    Since, area = πr², it will quadrupled.


  1. The area of the ring between two concentric circles, whose circumference are 88 cm and 132 cm, is :









  1. View Hint View Answer Discuss in Forum


    According to question, Circumference of outer circle
    = 2πr = 132 cm

    ⇒ r =
    132
    × 7 = 21 cm
    2 × 22

    Circumference of inner circle = 2πr1 = 88cm
    ⇒ r1 =
    88
    × 7 = 14 cm
    2 × 22

    ∴ Area of outer circle = πr²
    =
    22
    × 21 × 21 = 1386 cm²
    7

    and Area of inner circle = πr1²
    =
    22
    × 21 × 21 = 1386 cm²
    7

    ∴ Area of ring = (1386 – 616) cm² = 770cm²

    Correct Option: B


    According to question, Circumference of outer circle
    = 2πr = 132 cm

    ⇒ r =
    132
    × 7 = 21 cm
    2 × 22

    Circumference of inner circle = 2πr1 = 88cm
    ⇒ r1 =
    88
    × 7 = 14 cm
    2 × 22

    ∴ Area of outer circle = πr²
    =
    22
    × 21 × 21 = 1386 cm²
    7

    and Area of inner circle = πr1²
    =
    22
    × 21 × 21 = 1386 cm²
    7

    ∴ Area of ring = (1386 – 616) cm² = 770cm²



  1. Three circles of radius 3.5 cm each are placed in such a way that each touches the other two. The area of the portion enclosed by the circles is









  1. View Hint View Answer Discuss in Forum

    Using Rule 6 and 17,

    Radius of each circle = 3.5 cm From the figure.
    ∆ ABC will be an equilateral triangle of side 7 cm each.
    Now, the required area = Area of DABC – 3× (Area of a sector of angle 60° in a circle of radius 3.5 cm)

    =
    3
    × (7)² - 3
    60
    ×
    22
    × (3.5)² cm²
    43607

    =
    49√3
    - 19.25 cm²
    4

    = [21.217 – 19.25] cm²
    = 1.967 cm²

    Correct Option: B

    Using Rule 6 and 17,

    Radius of each circle = 3.5 cm From the figure.
    ∆ ABC will be an equilateral triangle of side 7 cm each.
    Now, the required area = Area of DABC – 3× (Area of a sector of angle 60° in a circle of radius 3.5 cm)

    =
    3
    × (7)² - 3
    60
    ×
    22
    × (3.5)² cm²
    43607

    =
    49√3
    - 19.25 cm²
    4

    = [21.217 – 19.25] cm²
    = 1.967 cm²