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Quantitative Aptitude

VOLUME AND SURFACE AREA MCQs

Total Questions : 820 | Page 9 of 82 pages
Question 81.

Find the area of the rhombus if the length of each side be 7 cm. and corresponding altitude is 8 cm?

  1.    36 sq mt
  2.    44 sq mt
  3.    56 sq mt
  4.    66 sq mt
  5.    None of these
 Discuss Question
Answer: Option C. -> 56 sq mt
 -  area of rhombus = base × height = 7 cm × 8 cm = 56 sq cm
Question 82.

A solid cubical block of fine wood costs rupees 256 at rupees 500/m3. Find its volume and the length of each side?

  1.    50 cm
  2.    60 cm
  3.    70 cm
  4.    80 cm
  5.    None of these
 Discuss Question
Answer: Option D. -> 80 cm
 -    Let the edge of the cubical box be “a” m.
  Rs. 500 is the cost of 1 m3 wood
  Rs. 256. is the cost of 1x256/500 m3 wood=0.512m3
  So, Volume of total wood = 0.512m3
  a x a x a = 0.512m3
  a x a x a = 0.8 x 0.8 x0.8x
  The length of each side = 0.8m=80cm
Question 83.

What will be the volume of the cylinder in which area of the base is 45 sq.cm and height is 6 cm?

  1.    210
  2.    225
  3.    245
  4.    270
  5.    None of these
 Discuss Question
Answer: Option D. -> 270
 -    The volume of the cylinder = Area of base x height =45 sq.cm x 6 cm
  =270cm3
Question 84.

Area of 4 walls of a room is 108 m2 .If height and length of room is in ratio 2: 5 and height and breadth in ratio 4: 5. Find the area of floor of the room?

  1.    25 sq mt
  2.    35 sq mt
  3.    45 sq mt
  4.    55 sq mt
  5.    None of these
 Discuss Question
Answer: Option C. -> 45 sq mt
 -    Given: L : H = 5 : 2 Þ  H : B = 4 : 5
  L : H : B = 20 : 8 : 10
  Area of four walls of a room is =2(l + b) h = 108 Þ (l + b) h = 54
  (20 x + 10x) x 8x = 54
  240x2 = 54
  x2 = 54 / 240
  x2 = 0.225
  The area of floor of the room = l x b =l × b = 20x × 10x =200x2 =200x 225= 45m2
Question 85.

If Area of the square inscribed in a semicircle is 2cm2 .Find the area of the square inscribed in a full circle?

  1.    1 sq cm
  2.    3 sq cm
  3.    4 sq cm
  4.    5 sq cm
  5.    None of these
 Discuss Question
Answer: Option D. -> 5 sq cm
 -    Area of square = 2cm2
  Side of square = square root of 2
  Let r be the radius of the circle and adjust it like that it forms a right angle triangle then
  r2 = (square root of 2)2 + (square root of 2 / 2)2
  r2 = 2 + ( 2 / 4)
  r2 = 5 / 2
  r = square root of ( 5 / 2)
  In a full square the diagonal of square will be the diameter of the cirlcle.
  r = square root of ( 5 / 2) is this so diameter = 2 x square root of (5 / 2)
  Diagonal of square = side x square root of 2
  side x square root of 2 = 2 x square root of 5 / square root of 2
  side x 2 = 2 x square root of 5
  side = square root of 5
  Area of square = r2
  = (square root of 5)2
  = 5 cm2
Question 86.

A cylinder tube open at boyh ends is made of metal. The internal diameter of the tube is 11.2 cm and its length is 21 cm .The metal everywhere is 0.4 cm thick . Calculate the volume of the metal correct to 1 place of decimal?

  1.    306
  2.    306.2
  3.    406
  4.    406.2
  5.    None of these
 Discuss Question
Answer: Option B. -> 306.2
 -    Internal diameter = 11.2 cm
  Internal radius= 11.2/2 = 5.6 cm  Length of the tube = 21 cm
  Volume of the internal cylinder π r 2 h = 22x 5.6x5.6x21/7 =2069.76cm 2
  External radius, R = (5.6 + 0.4) cm = 6 cm
  Volume of the external cylinder = πR2 h =22x6x6x21/7=2376cm2
  Now, volume of the metal = Volume of the external diameter – Volume of the internal diameter 
  = (2376 – 2069.76) cm3 = 306.24 cm3 = 306.2 cm3
Question 87.

The dimension of an oil tin are 26 m x 26 cm x 45 cm .Find the area of the tin sheet required for making 20 such tins. If 1 square meter sheet costs Rs. 10 , find the total cost for making 20 such tins?

  1.    Rs 119.64
  2.    Rs 120
  3.    Rs 120.64
  4.    Rs 130
  5.    None of these
 Discuss Question
Answer: Option C. -> Rs 120.64
 -    Area of the tin sheet required =  Area of 20 oil tins
  = 20 × 2 (lb + bh + hl)   = 20x2(26x26+26x45+45x26)=12.06m2
  Cost of 1 m2 tin sheet = Rs.10
  Cost of  12.064 m2 tin sheet = Rs.10 2.064  = Rs.120.64
  So, total cost for making 20 such tins = Rs.120.64
Question 88.

In a shower, 5 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is:

  1.    75 cu. m
  2.    750 cu. m
  3.    7500 cu. m
  4.    75000 cu. m
  5.    None of thsee
 Discuss Question
Answer: Option B. -> 750 cu. m
 -  

1 hectare = 10,000 m2
So, Area = (1.5 x 10000) m2 = 15000 m2.
 

Depth = 5  m  =  1  m. 100 20

 

 Volume = (Area x Depth) =   15000 x 1 m3 = 750 m3. 20
Question 89.

66 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be:

  1.    84
  2.    90
  3.    136
  4.    168
  5.    None of these
 Discuss Question
Answer: Option A. -> 84
 -    Let the length of the wire be h.
  Radius = 1   mm   = 1   cm. Then, 2 20  
  22   x  1 x   1   x h = 66. 7 20 20  
 h =   66 x 20 x 20 x 7   = 8400 cm = 84 m. 22
Question 90.

A hollow iron pipe is 21 cm long and its external diameter is 8 cm. If the thickness of the pipe is 1 cm and iron weighs 8 g/cm3, then the weight of the pipe is:

  1.    3.6 kg
  2.    3.696 kg
  3.    36 kg
  4.    36.96 kg
  5.    None of these
 Discuss Question
Answer: Option B. -> 3.696 kg
 -    External radius = 4 cm,
  Internal radius = 3 cm.
  Volume of iron  =   22   x [(4)2 - (3)2] x 21 cm3 7  
  =   22 x 7 x 1 x 21 cm3 7
  = 462 cm3.
  Weight of iron = (462 x 8) gm = 3696 gm = 3.696 kg

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