Arithmatical - Volume and Surface Areas

DIRECTIONS : Problems based on Volume&Surface Areas.
10. Spheres A and B have their radil 40 cm and 10 cm respectively. The ratio of the surface area of A to the surface area of B is
  A.  1 : 4
  B.   1 : 16
  C.  4 : 1
  D.  16 : 1
Solution
Let the radil of A and B be r and R respectively.
Required ratio= 4Πr2/ 4ΠR2
‹=› r2 / R2
‹=› (r/R)2
‹=›(40/10)2
‹=› 16 : 1.
11. How many cubes of 10 cm edge can be put in a cubical box of 1 m edge?
  A.  10
  B.  100
  C.  1000
  D.  10000
Solution
Number of cubes= (100×100×100 /10×10×10)
‹=› 1000.

12. The cost of the paint is Rs. 36.50 per kg. If 1 kg of paint covers 16 squares feet, how much will it cost to paint outside of a cube having 8 feet each side?
  A.  Rs. 692
  B.  Rs. 768
  C.  Rs. 876
  D.  Rs. 972
Solution
Surface area of the cube = (6 ×82)sq.ft
= 384 sq.ft.
Quantity of paint required= (384 / 16)kg
‹=›24 kg.
Cost of painting = Rs.(36.50 ×24)
= Rs. 876.
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