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Aptitude Questions: Mensuration Set 8

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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 rectangle garden having length and breadth as 110 m and 65 m respectively has 2.5 m wide path around the sides inside the garden. Find the cost of gravelling the path at 50 paise per sq. metre.
    A) Rs 420
    B) Rs 325
    C) Rs 425
    D) Rs 405
    E) Rs 375
    C) Rs 425
    Explanation:

    Area of garden = 110*65 = 7150 m2
    Area of path = (110-5)*(65-5) = 6300 m2
    So area of path = 7150 – 6300 = 850 m2
    So cost = 850*(50/100) = Rs 425

  2. The cost of painting a triangular board at Rs 24.68 per m2 is Rs 33318. If the base of this board is thrice its height, find the height of the board.
    A) 66 m
    B) 75 m
    C) 30 m
    D) 90 m
    E) 45 m
    D) 90 m
    Explanation:

    Area of triangle = 33318/24.68 = 1350 m2
    If height is x, then base = 3x
    So (1/2)*3x*x = 1350
    x2 = 900, x = 30
    so base = 3*30 = 90

  3. The radius of a wheel of car is 70 cm. How many revolutions per minute the wheel will make in order to keep a speed of 66 km/hr?
    A) 234
    B) 272
    C) 225
    D) 300
    E) 250
    E) 250
    Explanation:

    Distance to be covered in 1 min = 66*(1000/60) = 1100 m
    70 cm = 0.70 m
    Circumference of wheel = 2*(22/7)*0.70 = 4.4 m
    Number of revolutions = (1100/4.4) = 250

  4. The length and breadth of a rectangle are in the ratio 3 : 2. If the length is increased by 5 m keeping the breadth same, the new area of rectangle is 2600 m2. What is the breadth of the rectangle?
    A) 30 m
    B) 20 m
    C) 32 m
    D) Cannot be determined
    E) None of these
    B) 20 m
    Explanation:

    3x, 2x
    So (3x+5)*2x = 2600
    6x2 + 10x = 2600
    3x2 + 5x – 1300 = 0
    3x2 – 60x + 65x – 1300 = 0
    3x(x-20) + 65(x-20) = 0
    Solve, x = 20
    So breadth = 20 m

  5. What will be the percentage increase in the surface area of the cube whose side is increased by 50%
    A) 75%
    B) 125%
    C) 150%
    D) 100%
    E) 92%
    B) 125%
    Explanation:

    Surface area of cube = 6a2
    A increases by 50%
    So area increases by 50 + 50 + (50)(50)/100 = 125%

  6. The radius of base and height of a cylinder are in the ratio 2 : 3. Find the total surface area of the cylinder if its volume is 12936 cm3.
    A) 3080 cm2
    B) 2680 cm2
    C) 4940 cm2
    D) 3280 cm2
    E) None of these
    A) 3080 cm2
    Explanation:

    (22/7)*(2x)2*3x = 12936
    Solve, x = 7
    So radius = 7 cm, height = 21 cm
    Total surface area = 2*(22/7)*14*(21+14) = 3080

  7. The diameter and the height of a right circular cylinder are 11.2 cm and 21 cm respectively. The metal around its outer body is 0.4 cm thick. What is the volume of the metal?
    A) 186.34 cm3
    B) 306.24 cm3
    C) 156.56 cm3
    D) 336.24 cm3
    E) None of these
    B) 306.24 cm3
    Explanation:

    Internal radius = (11.2)/2 = 5.6, so outer radius = 5.6+0.4 = 6cm
    So volume of metal = (22/7)*62*21 – (22/7)*(5.6)2*21 = (22/7)*[62 – (5.6)2]*21

  8. What is the volume of a right circular cone whose radius of base is 70 cm and curved surface area is 40040 cm2?
    A) 839500 cm3
    B) 713400 cm3
    C) 862400 cm3
    D) 462320 cm3
    E) None of these
    C) 862400 cm3
    Explanation:

    r = 70
    (22/7)*70*l = 40040
    So l = 182
    h = √(182) 2 – 702 =168 cm
    so vol = (1/3)*(22/7)*702 *168

  9. Find the radius of each of the 8 spherical balls which are made from a solid sphere of radius 10 cm by melting it.
    A) 12 cm
    B) 8 cm
    C) 20 cm
    D) 5 cm
    E) 15 cm
    D) 5 cm
    Explanation:

    Volume of each of the 8 ball = [(4/3)*(22/7)*103]/8
    So (4/3)*(22/7)*r3 = [(4/3)*(22/7)*103]/8
    Solve, r = 5

  10. The metal used in the cylinder having external radius 6 cm, height 15 cm and thickness 0.25 cm is to be cast from a cylinder of radius 1 cm. What is the approximate height of the cylinder from which casting is to be done?
    A) 8 1/4 days
    B) 8 3/4 days
    C) 9 days
    D) 10 3/4 days
    E) 11 1/3 days
    B) 8 3/4 days
    Explanation:

    Volume of metal = (22/7)*[62 – (5.75)2]*15
    So (22/7)*12*h = (22/7)*[62 – (5.75)2]*15
    Solve, h ≈ 44