Quantitative Aptitude: Mensuration Questions Set 9

  1. The ratio between the perimeter and the breadth of a rectangle is 26 : 5. If the area of the rectangle is 1000 sq. cm, what is the length of the rectangle?
    45cm
    35cm
    40cm
    30cm
    None
    Option C
    Solution:
    2(l+b):b=26:5
    10l+10b=26b
    10l=16b
    b=5/8l
    Area lb=1000
    l*5/8l=1000
    l2=1600
    l=40cm.
  2. A cistern 6m long and 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is:
    49m2
    53m2
    38m2
    40m2
    None
    Option A
    Solution:
    Area=[2(lb+bh+hl)-lb] =2(bh+hl)+lb
    =[2(4*1.25 + 6*1.25) + (6*4)] =25+24
    =49m2.
  3. The radius of the base of a cylindrical Can is 140cm and its height is 240cm. It is full of Petrol. How many tins, each of size 25 cm × 22 cm × 30 cm can be filled with Petrol from the Can?
    896
    784
    852
    926
    None
    Option A
    Solution:
    Volume of Can=(22/7)*140*140*240
    =22*20*140*240
    Volume of a tin=25*22*30
    Number of tins=(22*20*140*240)/(25*22*30)
    =4*8*28=896.
  4. The length of a room is 6.5 m and width is 2.75 m. Find the cost of paying the floor by slabs at the rate of Rs. 400 per sq.metre.
    Rs7350
    Rs6100
    Rs7150
    Rs6450
    None
    Option C
    Solution:
    Area = 6.5 * 2.75
    Cost for 1 sq. metre. = Rs. 400
    Total cost = 6.5 * 2.75 * 400
    =Rs7150.
  5. The ratio of the radius and height of a cone is 7: 18. Its volume is 924 cm. Its radius and height is
    14cm, 36cm
    21cm, 54cm
    7cm, 18cm
    28cm, 72cm
    None
    Option C
    Solution:
    Radius:Height=7x:18x
    Volume of cone 1/3*22/7*7x*7x*18x=92
    22*6*7x=924
    x=1.
    Then r=7, h=18.
  6. The diagonal of a rectangle is √125 cm and its area is 50 sq. cm. The perimeter of the rectangle must be:
    45cm
    30cm
    42cm
    36cm
    None
    Option B
    Solution:
    √(l2 + b2)=√125
    lb=50
    (l+b)2=l2=+b2=+2lb
    =125+(2*50)
    =225.
    L+b=15
    Perimeter=2*15=30cm.
  7. A rectangular block of metal has dimensions 21 cm*77 cm*24 cm. The block has been melted into a sphere. The radius of the sphere is
    28cm
    21cm
    32cm
    18cm
    None
    Option B
    Solution:
    Volume of the sphere=4/3*22/7*r3
    4/3*22/7*r3=21*77*24
    r3=(21*77*24*3*7)/(4*22)
    =33 * 73
    r=3*7=21cm.
  8. The perimeter of a square is equal to twice the perimeter of a rectangle of length of 8 cm and breadth 7 cm. What is the circumference of a semicircle whose diameter is equal to the side of the square?
    34.6cm
    36cm
    38cm
    38.5cm
    None
    Option D
    Solution:
    Perimeter of rectangle = 2(l+b) = 2(8+7)= 30cm
    Perimeter of square is twice the perimeter of rectangle = 2*30= 60cm
    Then, side of the square is = 1/4 x 60 = 15cm.
    Circumference of the semicircle =πr + 2r
    =22/7*15/2 +2*15/2
    =23.5+15
    =38.5cm.
  9. Surface area of a cube is 2400 cm 2. Find out the length of its diagonal.
    16√3cm
    20√3cm
    24√3cm
    26√3cm
    None
    Option B
    Solution:
    Surface area of cube 6*side2
    6*side2=2400
    side2=2400/6=400
    side=20cm.
    Diagonal of cube=√3*side=20√3cm.
  10. The radius of a circular field is equal to the side of a square field. If the difference between the perimeter of the circular field and that of the square field is 48m, what is the side of the square field?
    26m
    31m
    24m
    21m
    None
    Option D
    Solution:
    Radius of circular field=side of square field
    2*22/7a – 4a=48
    (44-28)a=(48*7)
    16a=48*7
    a=21m.



 

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