Aptitude  Volume and Surface Area
Exercise : Volume and Surface Area  General Questions
 Volume and Surface Area  Formulas
 Volume and Surface Area  General Questions
 Volume and Surface Area  Data Sufficiency 1
 Volume and Surface Area  Data Sufficiency 2
11.
The curved surface area of a cylindrical pillar is 264 m^{2} and its volume is 924 m^{3}. Find the ratio of its diameter to its height.
Answer: Option
Explanation:
r^{2}h  =  924  r =  924  x 2  = 7 m.  
2rh  264  264 
And, 2rh = 264 h =  264 x  7  x  1  x  1  = 6m.  
22  2  7 
Required ratio =  2r  =  14  = 7 : 3. 
h  6 
12.
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:
Answer: Option
Explanation:
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 
x = 10 cm = 1 dm.
13.
What is the total surface area of a right circular cone of height 14 cm and base radius 7 cm?
Answer: Option
Explanation:
h = 14 cm, r = 7 cm.
So, l = (7)^{2} + (14)^{2} = 245 = 75 cm.
Total surface area  = rl + r^{2}  


= [154(5 + 1)] cm^{2}  
= (154 x 3.236) cm^{2}  
= 498.35 cm^{2}. 
14.
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?
Answer: Option
Explanation:
Volume of the large cube = (3^{3} + 4^{3} + 5^{3}) = 216 cm^{3}.
Let the edge of the large cube be a.
So, a^{3} = 216 a = 6 cm.
Required ratio =  6 x (3^{2} + 4^{2} + 5^{2})  =  50  = 25 : 18.  
6 x 6^{2}  36 
15.
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?
Answer: Option
Explanation:
Number of bricks =  Volume of the wall  =  800 x 600 x 22.5  = 6400.  
Volume of 1 brick  25 x 11.25 x 6 
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