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Maths / Surface Area and Volume / Volume of cylinder

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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,

Specific gravity of wood = $0.7;gm/cm^{3}$

and Specific gravity of wood graphite = $2.1;gm/cm^{3}$

So, weight of the pencil = Volume of wood X specific gravity of wood + Volume of graphite X specific gravity of graphite

= (5.28 X 0.7 + 0.11 X 2.1) gm

= 3.927 gm

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Volume of cylinder

₹10800 ₹6000 +
Taxes