Arithmatical - Volume and Surface Areas

DIRECTIONS : Problems based on Volume&Surface Areas.
1. 50 men took a dip in water tank 40 m long and 20 m broad on a religious day. If the average displacements of water by a man is 4 m3, then the rise in the water level in the tank will be
  A.  20 cm
  B.  25 cm
  C.  35 cm
  D.  50 cm
Solution
Total number of water displaced= (4 ×50)m3
‹=› 200m3
Rise in water level = (200 / 40×20)m
= 0.25 m
‹=› 25 cm
2. A cube of edge 5 cm is cut into cubes of each edge 1 cm. The ratio of the total surface area of one of the small cubes to that of the large cube is equal to
  A.  1 : 5
  B.  1 : 25
  C.  1 : 125
  D.  1 : 625
Solution
Required ratio=(6x1x1 / 6x5x5)
‹=› 1/ 25
‹=› 1 : 125.

3. The cost of painting the whole surface area of a cube at the rate of 13 paise per Sq.cm is Rs. 343.98. Then the volume of the cube is
  A.  8500 cm3
  B.  9000 cm3
  C.  9250 cm3
  D.  9261 cm3
Solution
Surface area= (34398 / 13)
‹=›2646cm3
‹=›6a2= 2646
‹=›a2= 441
‹=›a = 21.
So,volume =(21x21x21)cm3= 9261cm3.
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