Volume of cylinder


 
 
Concept Explanation
 

Volume of cylinder

Volume of A Cylinder: Volume of Cylinder = Measure of the space occupied by the cylinder

                                                               = The area of each circular sheet x  Height

                                                              = large pi r^2 h

Thus, Volume of a right circular cylinder = Area of the base x Height = large pi r^2h

Illustration: Find the volume of a right circular cylinder, if the radius of its base and height are 7 cm and 15 cm respectively.

Solution: We know that, Volume of cylinder = large pi r^2h .  Here,  r = 7cm and h = 15cm

Volume of cylinder =frac{22}{7}times 7^2times 15=22times 7times 15=2310cm^3

Illustration: A lead pencil consists of a cylinder of wood with a solid cylinder of graphite filled into it. The diameter of the pencil is 7mm, the diameter of the graphite is 1 mm and the length of the pencil is 14 cm. Find the:

(i) Volume of the graphite

(ii) Volume of the wood

(iii) The weight of the whole pencil, if the specific gravity of the wood is 0.7;gm/cm^{3} and that of the graphite is 2.1;gm/cm^{3}.

Solution: We have,

Diameter of the graphite cylinder = 1 mm = frac{1}{10};cm

So, radius of the graphite cylinder =frac{1}{20};cm

Length of the graphite cylinder = 14 cm

V_{1}= Volume of the graphite cylinder =frac{22}{7}times frac{1}{20}times frac{1}{20}times 14;cm^{3}

                                                              =0.11;cm^{3}

(ii) We have,

Diameter of the pencil = 7 mm =frac{7}{10};cm

So, radius of pencil =frac{7}{20};cm

Length of pencil = 14 cm

V_{2}= Volume of the pencil =frac{22}{7}times frac{7}{20}times frac{7}{20}times 14;cm^{3}

                                          =5.39;cm^{3}

Volume of the wood V_{2}-V_{1}=(5.39-0.11);cm^{3}

                                                 =5.28;cm^{3}

(iii) We have,

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Sample Questions
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Question : 1

If the volume and the radius of a cylinder are 41.58 cm cube and 2.1 cm respectively, then the height of the cylinder is :

Right Option : B
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Explanation
Question : 2

If the radius of a cylinder becomes half and the height gets doubled, what is the ratio of new volume of the cylinder to the original volume ?

Right Option : C
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Explanation
Question : 3

A conical vessel, with internal radius of the base 8 cm and height 42 cm is full of water. The water is poured in a right circular cylindrical vessel, the radius of its base is 16 cm, the height in cm of the water level in the cylindrical vessel is:

Right Option : D
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Explanation
 
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