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

The difference between inside and outside surfaces of a circular cylinder 14 cm long is 88 sqw.cm. If the volume of the tube is 176 cu cm, find the outer radius of the cylineder.

Right Option : B
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Explanation
Question : 2

A well with 14m diameter is 8m deep. The Earth taken out of it has been evenly spread all around it to a width of 21m to form an embankment. Find the height of the embankment in centimetre.

Right Option : C
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Explanation
Question : 3

The radius of the outer circumference of a cylindrical ring is 12 cm and the diameter of the cross section is 1.5 cm. Then the volume of circular ring is:

Right Option : B
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Explanation
 
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