Quantitative Aptitude: Mensuration Questions Set 14

  1. The perimeter of an equilateral triangle is equal to the perimeter of a square whose diagonal is 9√2 cm. Find out the area of the equilateral triangle ?
    48√3
    60√3
    30√3
    36√3
    20√3
    Option D
    side of square=9√2/√2=9
    let the side of equilateral triangle be x cm.
    3x=4*9
    x=12
    area of equilateral triangle= √3/4*12*12=36√3

     

  2. If ratio of height and radius of a cone is 5:6. Volume of cone is 480π cm^3, then find slant height of cone (in cm) ?
    2√61
    4√61
    8√50
    9√68
    10√52
    Option A
    let height and radius of cone be 5x and 6x.
    volume of cone =480π
    1/3*π*6x^2*5x=480π
    x^3=8
    x=2 cm
    height=10cm , radius=12 cm
    so, slant height of cone =√(r^2+h^2)
    = √(144+100)=√244=2√61

     

  3. Circumference of a circle A is 2 times perimeter of a square. Area of the square is 484 cm^2. What is the area of another circle B whose radius is half the radius of the circle A ?
    530
    640
    590
    616
    none of these
    Option D
    Area of the square =484cm
    side of square =22cm.
    perimeter of square =22*4=88cm.
    ATQ,
    circumference of a circle A=88*2 =176cm.
    2πr =176
    r=176*7/44 =28
    Radius of circle B= 28/2 =14cm.
    Area of circle B=22/7*14*14 =616cm^2

     

  4. If the length of a rectangular field is increased by 20% and the breadth is reduced by 20%, the area of the rectangle will be 288 m^2 . What is the area of the original rectangle ?
    400
    300
    520
    220
    none of these
    Option B
    Percentage change in area =
    +20-20-(20*20)/100 =-4%
    96%= 288
    100%=288/96*100= 300 m^2

     

  5. Side of a rhombus is 20cm and the ratio of diagonals of a rhombus is 3:4, then find the area of the rhombus .
    384
    264
    544
    288
    484
    Option A
    Side of rhombus =20cm.
    Let,
    two diagonals of a rhombus be 3x and 4x.
    side =√(3x)^2+(4x)^2
    = 9x^2+16x^2 =5x
    5x=20
    x=4
    two diagonals =(4*3*2) and (4*4*2) =24 and 32
    Area =1/2*24*32 =384 cm^2.

     

  6. The side of a square is 20% more than the side of an equilateral triangle whose perimeter is 75m. Find the ratio between perimeter of square to area of triangle.
    96:125√3
    48:55√3
    32:58
    96:130√3
    32:42
    Option A
    perimeter of triangle=75
    side of triangle=75/3=25m
    side of square=25*120/100=30 m
    perimeter of square=4*30=120 m
    area of triangle=√3/4*25*25=625√3/4 m^2
    ratio=120:625√3/4=480:625√3=96:125√3

     

  7. Radius of circular field is 40% more than length of a rectangular field, having the area 80 m^2. If circumference of a circle is 88m, then radius of circular field is what percent more than breadth of rectangular field ?
    60
    50
    120
    75
    100
    Option D
    let radius of circle =7x
    and length of rectangular field=10m
    area of rectangular field=80 m^2
    10*breadth=80
    breadth=8m
    required percentage=14-8?8*100=6/8*100=75%

     

  8. Perimeter of a circle is 88cm. Find volume of a cylindrical vessel whose radius is equal to the radius of circle and height of cylindrical vessel is 20 cm.
    15000
    12320
    14220
    16780
    20400
    Option B
    Perimeter of circle =88
    r=88*7/44=14 cm
    radius of cylindrical vessel =22/7*14*14*20 = 12320 cm^2

     

  9. The ratio between length and breadth of a rectangular field is 5:4 . If area of rectangular field is 320 m^2, then find the perimeter of rectangular field.
    64
    40
    100
    72
    84
    Option D
    Let length of field =5x
    breadth of field =4x
    ATQ,
    5x*4x =320
    20x^2=320
    x^2 =320/20 =16
    x=4
    Perimeter =2(5x+4x) =18x =18*4= 72

     

  10. The total area of a circle and a square is equal to 1241 cm^2. The diameter of the circle is 28cm. What is the sum of the circumference of the circle and the perimeter of the square ?
    132
    188
    192
    288
    196
    Option B
    diameter of circle=28cm
    radius=14cm
    area of circle=22/7*14*14=616
    ATQ,πr^2+a^2=1241
    a^2=1241-616=625
    a=25
    circumference of the circle=2*22/7*14=88
    perimeter of square=4a=4*25=100
    sum=88+100=188

     

 

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