Quantitative Aptitude: Mensuration Questions Set 15

  1. The ratio of length and breadth of rectangular field is 3 : 2. If the perimeter of rectangular field is 40cm, then what is the area of square whose side 5cm more than the length of rectangular field ?
    216
    289
    324
    196
    400
    Option B
    Let length and breadth or rectangular field = 3x and 2x
    perimeter = 40
    2(3x + 2x) = 40
    10x = 40
    x = 4
    length = 3 * 4 = 12cm
    side of square = 12 + 5 = 17
    Area of square = 17 * 17 = 289 cm^2

     

  2. Length of two rectangles A and B is 14 cm and 20 cm respectively and sum of their breadth 14 cm. If ratio of perimeter of A and B is 5 : 7, then what is the difference between area of these rectangles ?
    84
    54
    42
    62
    76
    Option E
    Let breadth of rectangular A = x
    and breadth rectangular B = 14 – x
    perimeter of rectangular A = 2 (14 + x)
    perimeter of rectangle B = 2 (20 + 14 – x)
    = 2 (34 – x)
    2 (14 + x)/2 (34 – x) = 5/7
    340 – 10x = 196 + 14x
    x = 6
    breadth of rectangle A = 6 cm
    breadth of rectangle B = 14 – 6 = 8 cm
    Area of rectangle A = 14 * 6 = 84 cm^2
    Area of rectangle B = 20 * 8 = 160 cm^2
    Difference = 160 – 84 = 76 cm^2

     

  3. If the diagonal of a cube is of length ‘x’, then what is the lateral surface area of that cube ?
    2x^2/3
    5x/3
    4x/3
    4x^2/3
    8x
    Option D
    Diagonal of cube = a√3
    a√3 = x
    a = x/√3
    lateral surface area = 4a^2 = 4*(x/√3)^2 = 4x^2/3

     

  4. If the total surface area of a cube is 8664 cm^2, the what is the length of its diagonal ?
    46√3
    34√3
    38√3
    24√3
    19√2
    Option C
    T.S.A = 8664
    6a^2 = 8664
    a^2 = 1444
    a = 38
    diagonal = a√3 = 38√3

     

  5. If the ratio of radius of two spheres A and B is 3 : 5, then what is the ratio of their volumes ?
    27 : 125
    3 : 5
    12 : 25
    9 : 25
    6 : 15
    Option A
    Ratio of volume of A and B = 4/3π(3)^3 : 4/3π(5)^3
    = 27 : 125

     

  6. The ratio of length and breadth of rectangles is 5 : 3 and its area is 240 m^2. If the perimeter of square is 8m less than the perimeter of rectangles, then what is the area of square ?
    324
    196
    1024
    1444
    1296
    Option B
    Let length and breadth of rectangles = 5x and 3x
    Area = 240
    15x^2 = 240
    x = 4
    length = 5 * 4 = 20
    breadth = 3 * 4 = 12
    perimeter of rectangle = 2 (20+ 12) = 64
    perimeter of square = 64 – 8 = 56
    side of square = 56/4 = 14
    Area of square = 14 * 14 = 196

     

  7. The non – parallel sides of a trapezium are equal to side of perimeter of square 40cm and the parallel sides are 8cm and 20cm respectively, find the perimeter of trapezium ?
    38
    24
    20
    36
    40
    Option D
    perimeter of square = 40
    side of square = 40/4 = 10cm
    non-parallel side of trapezium = 10
    one parallel side = 8cm
    other parallel side = 20cm
    breadth of tringle = 20 – 8/2 = 6
    let height of trapezium = h
    10^2 = h^2 + 6^2
    h^2 = 64
    h = 8
    perimeter = 10 + 10 + 8 + 8 = 36 cm

     

  8. The circumference of a circle A is equal to the perimeter of a square whose area is 1936 m^2. Diameter of circle B is four times the radius of circle A what is the area of circle B ?
    4532
    3952
    2840
    4900
    9856
    Option E
    Area of square = 1936 m^2
    side of square = √1936 = 44m
    perimeter of square = 44 * 4 = 176m
    2πr = 176
    r = 176 *7 /44 = 28
    diameter of circle B = 28 * 4 = 112
    radius = 112/2 = 56m
    Area = πr^2 = 22/7 * 56 * 56 = 9856

     

  9. If the height and radius of a cylinder increased by 25% and 20% respectively. Then what is the change in percent in its curved surface area ?
    20%
    50%
    40%
    25%
    58%
    Option B
    Let the height of cylinder = 4h
    increased height = 4h* 125/100 = 5h
    and radius of cylinder = 5r
    increased radius = 5r * 120/100 = 6r
    initial curved surface area = 2 * π * 4h * 5r = 40πhr
    new curved surface area = 2 * π * 5h * 6r = 60πhr
    % change = 60πhr – 40πhr/40πhr * 100 = 50%

     

  10. The length , breadth and height of a cuboid is 14m, 15m, 20m respectively,. Find the lateral surface area of cuboid ?
    1225
    1160
    4250
    2420
    3840
    Option B
    L.S.A = 2 * 20 (14 + 15) = 40 * 29 = 1160 m

     

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