Quantitative Aptitude: Mensuration Questions Set 10

  1. The side of the square exceeds the side of another square by 6cm and the sum of the areas of the two squares is 260cm2. The dimensions of the squares is
    6cm and 12cm
    8cm and 14 cm
    10cm and 16cm
    5cm and 11cm
    None
    Option B
    Solution:
    Let the side of the square=x cm
    Side of another square = x+6 cm
    x2 + (x+6)2 =260
    x2 +6x -112=0
    x=-14, 8(negative value neglected)
    x=8cm.
    Another square 8+6=14cm.
  2. A lawn is in the shape of rectangle of length 30m and width 20m inside the lawn there is a footpath of uniform width 2m bordering the lawn. The area of the path is.
    142m2
    154m2
    165m2
    184m2
    None
    Option D
    Solution:
    Area of the outer rectangle=30*20
    =600m2.
    Width of path is 2m.
    Inner length=30-4=26m
    Breadth=20-4=16m
    Inner rectangle area=26*16
    =416m2.
    Then Area of the path =600-416
    =184m2.
  3. The diameter of the wheel of a car is 140cm. Then, in order to keep the speed of 66km/hr. How many revolutions per minute must the wheel make?
    250
    180
    220
    195
    None
    Option A
    Solution:
    Radius of the wheel =70cm=0.7m
    Circumference=2*22/7*0.7
    =4.4m
    Distance to be covered in 1 min =(66*1000)/60
    =1100m.
    Then no of revolutions per minute=1100/4.4
    =250.
  4. The length and breadth of a rectangular park are in the ratio 7:3. A path, 2.5m wide running all around the outside of the park has an area of 275m2. The dimensions of the park
    28m, 12m
    21m, 9m
    35m, 15m
    56m, 24m
    None
    Option C
    Solution:
    Area of the park =7x *3x=21x2
    Length including the path =7x+5
    Breadth including the path =3x+5
    Area=(7x+5) * (3x+5)
    =21x2 +50x+25
    Now, 21x2 +50x+25-21x2 =275
    50x=250
    x=5.
    Then l=7*5=35m
    B=3*5=15m.
  5. Two circle touch externally. The sum of their areas is 169π and the distance between their centres is 17cm. The radius of the circles are
    10cm, 4cm
    12cm, 5cm
    15cm, 8cm
    8cm, 4cm
    None
    Option B
    Solution:
    Let the radius of the circles be x, 17-x
    Sum of the area = π x2 + π(17-x) 2
    π x2 + π(17-x) 2=169π
    2πx2-34πx+120π=0
    x2-17x+60=0
    x=12 or 5.
    Radius=12cm, 5cm.
  6. A metallic sheet is of rectangular shape with dimensions 45cm *32cm from each of its corners a square of 5cm is cut off. An open box is made of the remaining sheet. What is the volume of the box?
    3360cm3
    2850cm3
    2560cm3
    3850cm3
    None
    Option D
    Solution:
    L=45cm
    B=32cm
    Square of side 5cm is cut off from each corner
    Then length= 45 –(5+5)=35cm
    Breadth=32 –(5+5)=22cm
    And height of the box=5cm.
    Volume of the box=35*22*5
    =3850cm3.
  7. The radius and the height of a right circular cone are in the ratio 5:12. If its volume is 314m3, the slant height and the radius are
    13m
    21m
    18m
    24m
    None
    Option A
    Solution:
    r=5x and h=12x
    Volume of the cone=314 =1/3πr2h
    1/3*3.14 *5x2*12x=314
    314x3=314
    x=1.
    Then r=5m h=12m
    Slant height=√(r2 +h2)
    =√(25+144)
    =√169=13m.
  8. A 8cm cube is cut into 2cm cubes. What is the ratio of surface area of small cubes to that of the large cube?
    3:2
    4:3
    4:1
    5:2
    None
    Option C
    Solution:
    No of small cubes= Volume of large cube/volume of a small cube
    =83/23
    =64.
    Total surface area of large cube=6*82=384cm2
    Total surface area of 1 small cube=6*22=24cm2
    Total surface area of 64 small cube=64*24=1536cm2
    Ratio 1536:384
    =4:1.
  9. The area of a rectangle is 72 m2 and its length is 2 times is breadth. What is the perimeter of the rectangle?
    42m
    36m
    30m
    Data Inadequate
    None
    Option B
    Solution:
    Let the breadth be x
    Then
    x*2x=72
    x = 6 m
    then l=12m and b=6m
    Perimeter=2(12+6)
    =36m.
  10. The length of a rectangular floor is twice its breadth. If Rs.450 is required to paint the floor at the rate of Rs.1 per square metre, then what would be the length of floor?
    28m
    34m
    26m
    30m
    None
    Option D
    Solution:
    To paint per square metre for Rs 1.
    Then 450m2 is the area of the floor.
    Let the breadth be x.
    x*2x=450
    2x2=450
    x2=225
    x=15.
    Length=2*15=30m.


 

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