Volume of Hollow Cylinder


 
 
Concept Explanation
 

Volume of Hollow Cylinder

Let R and r be the external and internal radii of a hollow cylinder and h be its height as shown in the following figure. Then,

Volume of the material = Exterior volume  - Interior Volume

                                =pi R^{2}h-pi r^{2}h

                                =pi left (R^{2}- r^{2} right )h

Illustration: A cylindrical road roller made of iron is 1 m wide. Its inner diameter is 54 cm and thickness of the iron sheet rolled into the road roller is 9 cm. find the weight of the roller if 1 c.c of iron weighs 8 gm.

Solution: The width of the road roller is 1 m i.e.100 cm

So, Height(Length) of the cylinder = 100 cm

Inner radius of the cylinder  =r=frac{54}{2}=27;cm

Thickness of the iron sheet = 9 cm

So, Outer radius of the cylinder = R = (27 + 9) = 36 cm

Thus, volume of the iron sheet used = left ( pi R^{2}h-pi r^{2}h right );cm^{3}

                                                     =pi left (R^{2}- r^{2} right )h

                                                     =left [ pi (R+r)(R-r) hright ]

                                                     =left [ 3.14times (36+27)(36-27) times 100right ]

                                                    =frac{314}{100}times 63times 9times 100

                                                   =178038;cm^{3}

As we know that Weight = Volume X Density

So, Weight of the roller = 178038 X 8 gms

                                  =178038times frac{8}{1000};kgs

                                 =1424.304;kgs

Sample Questions
(More Questions for each concept available in Login)
Question : 1

A hollow cylindrical pipe is 21 dm long. Its outer and inner diameters are 8 cm and 6 cm respectively. Find the volume of the copper used in making the pipe.

Right Option : B
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Explanation
Question : 2

A cylinder tube, open at both ends, is made of metal. The internal diameter of the tube is 10.4 cm and its length is 25 cm. The thickness of the metal is 8 mm everywhere . Calculate the volume of the metal.

Right Option : B
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Explanation
Question : 3

The thickness of the metallic tube is 1 cm and the inner diameter of the tube is 12 cm. Find the  weight of 1 m long tube, if the density of the metal be 7.8;gm/cm^{3}.

Right Option : A
View Explanation
Explanation
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