Quantitative Aptitude: Mensuration Questions Set 16

  1. If the length of a rectangular field is increased by 15% and breadth is also increased by 10%, the area of the rectangle will be 253 m^2. What is the area of the original area of rectangle ?
    400
    240
    350
    180
    200
    Option E
    let original area of rectangle =100
    percentage change in area=15+10+15*10/100=26.5
    126.5=253
    original area=253/126.5*100=200 m^2

     

  2. The side of square is 25% more than the length of rectangular and perimeter of square is 80cm. Ratio of length and breadth of rectangular is 4:3, then find the area of rectangular.
    192
    215
    180
    220
    240
    Option A
    let the length of rectangular=4x
    side of square=5x
    perimeter of square=5x*4=20x
    20x=80
    x=4
    length of rectangular=4*4=16
    ratio of length and breadth=4:3
    breadth=16/4*3=12
    area of rectangular=16*12=192 cm^2

     

  3. The area of square 50m^2 less than the area of a rectangular, whose breadth is 12m. If the perimeter of a square is 40m, then find the perimeter of a rectangular.
    50
    49
    60
    65
    70
    Option B
    perimeter of square=40
    side of square=40/4=10m
    area of square=10^2=100
    area of rectangular=100+50=150m^2
    breadth=12m
    length=150/12=12.5m
    perimeter=2(12.5+12)=49

     

  4. The area of the square is in the ratio of 1444:1296. What will be the ratio of their perimeter ?
    20:21
    19:18
    22:25
    23:24
    18:19
    Option B
    The ratio of area= 1444:1296
    a^2:b^2=38:36=19:18
    ratio of their perimeter=19*4:18*4=19:18

     

  5. The side of square is 5cm more than the radius of a circle. The area of the circle is 154cm^2. What is the perimeter of the square ?
    44
    64
    56
    48
    52
    Option D
    area of the circle=154cm^2
    πr^2=154
    r^2=49
    r=7
    side of square=7+5=12cm
    perimeter of square=12*4=48cm

     

  6. The length of rectangular is 18cm which is 4cm more than diameter of a circle. What is the area of the circle ?
    154
    240
    150
    176
    198
    Option A
    diameter of circle=18-4=14
    2r=14
    r=7
    area of the circle=πr^2=22/7*7*7=154cm^2

     

  7. There is a rectangular field of 40cm in length and 30cm in breadth. On the inside of which a 5cm wide road, then find the area of road.
    800
    500
    700
    600
    1000
    Option D
    area of the outside rectangular field=40*30=1200cm^2
    length of inside rectangular=40-10=30
    breadth of the inside rectangular=30-10=20
    area of the inside rectangular=30*20=600
    the area of the road=1200-600=600cm^2

     

  8. The height and radius of a cylinder is 21cm and 12cm respectively. Find the volume of cone.
    4268
    3168
    4360
    4530
    4840
    Option B
    height of the cylinder=21cm
    radius of the cylinder=12cm
    volume of the cylinder=22/7*12*12*21=22*144*3
    volume of the cone=1/3*volume of cylinder
    =1/3*22*144*3=3168cm^2

     

  9. The ratio of the length of the diagonals of a rhombus is 4:3. If the perimeter of the rhombus is 160m. What is the length of the diagonal of a square whose area is same as that of rhombus ?
    15√3
    16√3
    20√2
    25√5
    24√2
    Option B
    let the diagonals of the rhombus be 4x and 3x
    side length of the rhombus=√(4x)^2+(3x)^2
    =√16x^2+9x^2
    =25x^2=5x
    perimeter=4*5x=20x=160
    20x=160
    x=8
    two diagonal of the rhombus=32 and 24
    area=1/2*32*24=384
    let the diagonal of the square=D
    side of the square=D/√2
    (D/√2)^2=384
    D^2/2=384
    D=16√3

     

  10. The circumference of the circle is 176cm and the radius of circle is 4 less than side of the square. Find the area of the square.
    576
    1000
    784
    1024
    1444
    Option D
    2πr=176
    r=176*7/44=28
    side of square=28+4=32
    area of square=32*32=1024

     

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