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Quantitative Aptitude

VOLUME AND SURFACE AREA MCQs

Total Questions : 820 | Page 10 of 82 pages
Question 91.

A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of the man is:

  1.    12 kg
  2.    60 kg
  3.    72 kg
  4.    96 kg
  5.    None of these
 Discuss Question
Answer: Option B. -> 60 kg
 -     Volume of water displaced = (3 x 2 x 0.01) m3
  = 0.06 m3.  
  Mass of man  = Volume of water displaced x Density of water
   = (0.06 x 1000) kg
   = 60 kg.
Question 92.

50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4 m3, then the rise in the water level in the tank will be:

  1.    10 cm
  2.    15 cm
  3.    20 cm
  4.    25 cm
  5.    None of these
 Discuss Question
Answer: Option D. -> 25 cm
 -  Total volume of water displaced = (4 x 50) m3 = 200 m3.
 Rise in water level =   200 m 0.25 m = 25 cm. 40 x 20
Question 93.

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:

  1.    49 sq mt
  2.    50 sq mt
  3.    53.5 sq mt
  4.    55 sq mt
  5.    None of these
 Discuss Question
Answer: Option A. -> 49 sq mt
 -     Area of the wet surface = [2(lb + bh + lh) - lb]
  = 2(bh + lh) + lb
  = [2 (4 x 1.25 + 6 x 1.25) + 6 x 4] m2
  = 49 m2.
Question 94.

A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m3) is:

  1.    4830
  2.    5120
  3.    6420
  4.    8960
  5.    None of these
 Discuss Question
Answer: Option B. -> 5120
 -    Clearly, l = (48 - 16)m = 32 m,
  b = (36 -16)m = 20 m,
  h = 8 m.
  Volume of the box = (32 x 20 x 8) m3 = 5120 m3
Question 95.

A cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.1 m and its walls are 5 cm thick. The thickness of the bottom is:

  1.    90 cm
  2.    1 dm
  3.    1 m
  4.    1.1 cm
  5.    None of these
 Discuss Question
Answer: Option B. -> 1 dm
 -    Let the thickness of the bottom be x cm.
  Then, [(330 - 10) x (260 - 10) x (110 - x)] = 8000 x 1000
  320 x 250 x (110 - x) = 8000 x 1000
  (110 - x) =  8000 x 1000  = 100 320 x 250
Question 96.

What is the total surface area of a right circular cone of height 14 cm and base radius 7 cm?

  1.    498.35 sq cm
  2.    498.35 sq m
  3.    502.35 sq cm
  4.    502.35 sq m
  5.    None of these
 Discuss Question
Answer: Option B. -> 498.35 sq m
 -  h = 14 cm, r = 7 cm.
So, l = (7)2 + (14)2 = 245 = 75 cm.
 Total surface area =22/7 (rl +  r2)   =   22 x 7 x 75 + 22 x 7 x 7  cm2 7 7
  = [154(5 + 1)] cm2
  = (154 x 3.236) cm2   = 498.35 cm2.
Question 97.

A large cube is formed from the material obtained by melting three smaller cubes of 3, 4 and 5 cm side. What is the ratio of the total surface areas of the smaller cubes and the large cube?

  1.    2 : 1
  2.    3 : 2
  3.    25 : 18
  4.    27 : 20
  5.    None of these
 Discuss Question
Answer: Option C. -> 25 : 18
 -    Volume of the large cube = (33 + 43 + 53) = 216 cm3.
  Let the edge of the large cube be a.
  So, a3 = 216           a = 6 cm.
  Required ratio =   6 x (32 + 42 + 52)   = 50 = 25 : 18. 6 x 62
Question 98.

How many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall of 8 m x 6 m x 22.5 cm?

  1.    5600
  2.    6000
  3.    6400
  4.    7200
  5.    None of these
 Discuss Question
Answer: Option C. -> 6400
 -   Number of bricks =    Volume of the wall =     800 x 600 x 22.5     = 6400. Volume of 1 brick 25 x 11.25 x 6
Question 99. A hollow spherical metallic ball has an external diameter 6 cm and is $$\frac{1}{2}$$ cm thick. The volume of metal used in the ball is :
  1.    $$37\frac{2}{3}{\text{ c}}{{\text{m}}^3}$$
  2.    $$40\frac{2}{3}{\text{ c}}{{\text{m}}^3}$$
  3.    $$41\frac{2}{3}{\text{ c}}{{\text{m}}^3}$$
  4.    $$47\frac{2}{3}{\text{ c}}{{\text{m}}^3}$$
 Discuss Question
Answer: Option D. -> $$47\frac{2}{3}{\text{ c}}{{\text{m}}^3}$$
Question 100. If a hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted into a cylinder of base diameter 8 cm, then the height of the cylinder is :
  1.    4 cm
  2.    $$\frac{13}{3}$$ cm
  3.    $$\frac{14}{3}$$ cm
  4.    5 cm
 Discuss Question
Answer: Option C. -> $$\frac{14}{3}$$ cm

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