Volume of Sphere


 
 
Concept Explanation
 

Volume of A Sphere

Volume of A Sphere: The volume V of a sphere of radius r is given by V=frac{4}{3}{pi}{r^3}; cubic ;units

Illustration: Find the volume of a sphere of radius 7cm.

Solution: We know that the volume V of a sphere of radius r is given by

V=frac{4}{3}{pi}{r^3}; cubic ;units

   =frac{4}{3} times {frac{22}{7}} times{7} times{7} times{7}

   =1437.33cm^3

Illustration: A solid lead ball of radius 7 cm was melted and then drawn into a wire of diameter 0.2 cm. Find the length of the wire.

Solution: We have,

Radius of the lead ball = 7 cm

As the ball is spherical, Volume of the lead ball =frac{4}{3}{pi}{r^3}

So, Volume of the lead ball =frac{4}{3}times frac{22}{7}times 7times 7times 7;cm^{3}

                                           =frac{4312}{3};cm^{3}

Clearly, the wire is a cylinder of radius 0.1 cm.

Let the length of the wire be h cm. Then,

Volume of the wlre =pi r^{2}h

Volume of the wlre =frac{22}{7}times 0.1times 0.1times h;cm^{3}

                             =frac{11h}{350};cm^{3}

But, Volume of the wire = Volume of the lead ball

                         frac{11h}{350}=frac{4312}{3}

h=frac{4312}{3}times frac{350}{11};cm

    =457.33;m

Hence, the length of the wire = 457.33 m

Illustration: A solid sphere of radius 1 cm is melted to stretch into a wire of length 100 cm. Find the radius of the wire.

Solution: We have,

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Sample Questions
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Question : 1

The curved surface area of a sphere is 1386 sq .cm. Its volume is ___________________

Right Option : C
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Explanation
Question : 2

A solid sphere of radius 3 cm is melted and then cast into small spherical balls each of diameter 0.6 cm. Find the number of balls thus obtained.

Right Option : C
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Explanation
Question : 3

Find the volume of the sphere of radius 0.7 cm.

Right Option : B
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Explanation
 
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