Area and Perimeter


  1. A wheel make 4000 revolution in moving a distance of 44 km. Find the radius of the wheel.











  1. View Hint View Answer Discuss in Forum

    Distance covered in 1 revolution
    = (44 x 1000) / 4000
    = 11 m

    According to the question,
    2πr = 11

    Correct Option: E

    Distance covered in 1 revolution
    = (44 x 1000) / 4000
    = 11 m

    According to the question,
    2πr = 11
    ⇒ (44/7) x r = 11
    ∴ r = (11 x 7) / 44 = 1.75 m


  1. If the area of a semi-circle be 77 sq m, find its perimeter.











  1. View Hint View Answer Discuss in Forum

    According to the question,
    Area of semi- circle = 77 m
    (1/2) x π x r2 = 77

    ∴Circumference of semi- circle =πr + 2r
    = ( π + 2)r

    Correct Option: A

    According to the question,
    Area of semi- circle = 77 m
    (1/2) x π x r2 = 77
    ⇒ r2 = (77 x 2 x 7)/22
    ∴ r = 7m

    ∴Circumference of semi- circle =πr + 2r
    = ( π + 2)r
    = [(22/7) + 2] x 7
    = 36 m



  1. A railing of 288 m is required for fencing a semi-circular park. Find the area of the park. (π = 22/7)









  1. View Hint View Answer Discuss in Forum

    Let the radius of the park be r, then
    πr + 2r = 288

    Area of the park = (1/2)πr2

    Correct Option: A

    Let the radius of the park be r, then
    πr + 2r = 288
    (π + 2)r = 288
    ⇒ [(22/7) + 2]r = 288
    ⇒ r = (288 x 7)/36 = 56

    ∴ Area of the park = (1/2)πr2
    = (1/2) x (22/7) x 56 x 56
    = 4928


  1. If the radius of a circle is increased by 6%, find the percentage increase in its area.









  1. View Hint View Answer Discuss in Forum

    Given that, a = 6
    According to the formula,
    Percentage increase in area
    = 2a + [a2/100]%

    Correct Option: B

    Given that, a = 6
    According to the formula,
    Percentage increase in area
    = 2a + [a2/100]%
    = 2 x 6 + [36/100]%
    = (12 + 0.36)%
    = 12.36%



  1. The wheel of an engine turns 350 times round its axle to cover a distance of 1.76 km. The diameter of the wheel is









  1. View Hint View Answer Discuss in Forum

    Distance covered in 1 round
    = (Total Distance) / (Total round)

    Correct Option: D

    Distance covered in 1 round
    = (Total Distance) / (Total round)
    = (1.76 x 1000)/350
    = 176/35 m

    ∴ 2πr = (1.76 x 100) / 35 cm
    2π = Diameter = 17600 x 7/22 x 35 = 160 cm