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Aptitude Questions – Mensuration Set 18

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Hello Aspirants. Welcome to Online Quantitative Aptitude section in AffairsCloud.com. Here we are creating question sample from Mensuration that are important for all the competitive exams. We have included some questions that are repeatedly asked in exams !!

  1. A cylindrical cistern whose diameter is 14 cm is partly filled with water. If a rectangular block of iron 22 cm in length, 18 cm in breadth and 7 cm in thickness is wholly immersed in water, by how many cm will the water level rise?
    A. 10 cm
    B. 18 cm
    C. 12 cm
    D. 16 cm
    E. None of these
    Answer – B. 18 cm
    Explanation :
    Volume of the Rectangular Block = 22 * 18 * 7
    Radius of the Cistern = 7 cm
    Area of the Cylinder = Π * r² * h = 22/7 * 7 * 7 * h
    22/7 * 7 * 7 * h = 22 * 18 * 7; h = 18 cm

  2. If the radius of cylinder is doubled, but height is reduced by 50%. What is the percentage change in volume?
    A. 100%
    B. 150%
    C. 125%
    D. 175%
    5. None of these
    Answer – A. 100%
    Explanation :
    R1/R2 = R/2R & H1/H2 = H/H/2
    Original Volume = πr²h
    New Volume = π(2r)²h/2
    Change in Volume = (2 – 1)/1 * 100 = 100

  3. The perimeter of a rectangle and a square is 80 cm each. If the difference between their areas is 100 cm. Find the sides of the rectangle.
    A. 30cm, 10cm
    B. 40cm, 15cm
    C. 25cm, 10cm
    D. 20cm, 30cm
    E. None of the Above
    Answer – A. 30cm, 10cm
    Explanation :
    2(l + b) = 4a = 80
    l + b = 40; a = 20 => a² = 400
    a² – lb = 100; 400 – lb =100; lb = 300
    (l – b)² = (l + b)² – 4lb
    (l – b)² = 1600 – 1200; l – b = 20;

  4. The length of a wall is 5/4 times of its height. If the area of wall will be 500m². What is the sum of the length and height of the wall?
    A. 55m
    B. 45m
    C. 40m
    D. 50m
    E. None of these
    Answer – B. 45m
    Explanation :
    l = 5x; h = 4x ; l * h = 500
    20x² = 500 ; x = 5
    l + h = 25 + 20 = 45m

  5. A circular path runs round a circular garden. If the difference between the circumference of the outer circle and inner circle is 88m. Find the width of Path?
    A. 14 m
    B. 15 m
    C. 18 m
    D. 13 m
    E. None of the Above
    Answer – A. 14 m
    Explanation :
    Width of the Road = R – r
    2πR – 2πr = 88
    R – r = 14 m

  6. The radius of a circle is 4 m. What is the radius of another circle whose area is 16 times of that first?
    A. 16 m
    B. 64 m
    C. 256 m
    D. 400 m
    E. None of these
    Answer – A. 16 m
    Explanation :
    Ratio of areas = (ratio of radii)²
    16/1 = (ratio of radii)²
    ratio of radii = 4/1
    The required radius = 16 m

  7. What is the radius of the circle whose area is equal to the sum of the areas of two circles whose radii are 20 cm and 21 cm?
    A. 27m
    B. 28m
    C. 29m
    D. 25m
    E. 15m
    Answer – C. 29m
    Explanation :
    πR² = πr1² + πr2²
    πR² = π(r1² + r2²)
    R² = (400 + 441)
    R = 29

  8. Find the area of a white sheet required to prepare a cone with a height of 21cm amd the radius of 20cm.
    A. 3080 cm²
    B. 2300 cm²
    C. 3460 cm²
    D. 3600 cm²
    E. None of these
    Answer – A. 3080 cm²
    Explanation :
    r = 20 ; h = 21
    l = √(400 + 441) = 29 cm
    Total surface area = πrl + πr² = πr(l + r) = 22/7 * 20(49) = 3080 cm²

  9. A hollow cylindrical tube open at both ends is made of plastic 4 cm thick. If the external diameter be 54 cm and the length of the tube be 490 cm, find the volume of plastic.
    A. 320000 cm³
    B. 340000 cm³
    C. 306300 cm³
    D. 308000 cm³
    E. None of these
    Answer – B. 640640 cm³
    Explanation :
    Explanation :
    External Radius = 27; Internal Radius = 23
    Volume of Plastic =πh(R² – r²) = 22/7 * 490(27² – 23²) = 308000 cm³

  10. A solid metallic cylinder of base radius 5 cm and height 7 cm is melted to form cones, each of height 1 cm and base radius 1 mm. Find the number of cones?
    A. 53500
    B. 49500
    C. 51500
    D. 52500
    E. None of these
    Answer – D. 52500
    Explanation :
    Explanation :
    Number of cones =Volume of Cylinder / Volume of one cone
    = π*5*5*7 / (1/3π * 1/10 * 1/10 * 1)
    = 52500