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Find the amount of water displaced by a solid spherical ball of diameter 
28 cm

Diameter = 28 cm

therefore  Radius (r) = 28 over 2 space c m space equals space 14 space c m

therefore  Amount of water displaced = 4 over 3 πr cubed

         equals 4 over 3 cross times 22 over 7 left parenthesis 14 right parenthesis cubed equals 34496 over 3 space cm cubed
equals space 11498 2 over 3 space cm cubed
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The diameter of the moon is approximately one-fourth of the diameter of the earth. What fraction of the volume of the earth is the volume of the moon?

Let the radius of the earth be r.
Then, diameter of the earth = 2r

therefore space Diameter of the moon equals 1 fourth left parenthesis 2 straight r right parenthesis equals straight r over 2

therefore  Radius of the moon = 1 half open parentheses r over 2 close parentheses equals r over 4

Volume of the earth (v1) = 4 over 3 πr cubed
Volume of the moon (v2)

equals 4 over 3 straight pi open parentheses straight r over 4 close parentheses cubed equals 1 over 64 open parentheses 4 over 3 πr cubed close parentheses

equals 1 over 64 (volume of the earth)

Hence, the volume of the moon is 1 over 64 th fraction of the volume of the earth.

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How many litres of milk can a hemispherical bowl of diameter 10.5 cm hold?

Diameter = 10.5 cm

therefore Radius (r) = fraction numerator 10.5 over denominator 2 end fraction equals 5.25 space cm


therefore  Amount of milk = 2 over 3 πr cubed

                 equals 2 over 3 cross times 22 over 7 cross times left parenthesis 5.25 right parenthesis cubed space cm cubed
 
                  = 303 cm3 (approx.)
                  = 0.303 l (approx.)
          
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The diameter of a metallic ball is 4.2 cm. What is the mass of the ball, if the density of the metal is 8.9 g per cm3?


Diameter = 4.2 cm


therefore  Radius (r) = fraction numerator 4.2 over denominator 2 end fraction space cm equals 2.1 space cm

therefore   Volume = 4 over 3 πr squared

             equals 4 over 3 cross times 22 over 7 cross times left parenthesis 2.1 right parenthesis cubed equals 38.808 space cm cubed

Density = 8.9 g per cm3
Mass of the ball = Volume x Density
= 38.808 x 8.9 = 345.39 g (approx.).

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Find the amount of water displaced by a solid spherical ball of diameter 
0.21 m.

Diameter = 0.21 m.

therefore  Radius (r) = fraction numerator 0.21 over denominator 2 end fraction space straight m equals 0.105 space straight m
therefore  Amount of water displaced = 4 over 3 πr cubed
           equals 4 over 3 cross times 22 over 7 cross times left parenthesis 0.105 right parenthesis cubed equals 0.004851 space straight m cubed.
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