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Sphere: Surface Area & Volume
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Sphere
For a sphere of radius r, we have
(i) Surface area = 4r2
(ii) Volume = (4/3)r3

For a hemi-sphere of radius r, we have
(iii) Surface area = 2r2
(iv) Total surface area = 2r2 + r2 = 3 r2
(v) Volume = (2/3)r3.
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Example: A sphere of diameter 12 cm is dropped in a right circular cylindrical vessel partly filled with water. The diameter of the cylindrical vessel is 24 cm. If the sphere is completely submerged in water, by how much will the level of water rise in the cylindrical vessel?
Solution: Given:
Radius of the sphere = 6 cm.
Volume of the sphere = (4/3) x (6)3 cm3 = 288 cm3
Radius of the cylindrical vessel = 12 cm.

Suppose water level rises by h cm in the cylindrical vessel. Then,
Volume of the cylinder of height h cm and radius 5 cm = (x 122 x h) cm3
= 144 h cm3

Clearly, volume of water displaced by the sphere is equal to the volume of the sphere. 
Therefore,  288 h = 144  
h = 1/2 cm
Hence, water level rises by 1/2 cm.
 
   
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