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

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
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Explanation
Question : 2

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 : 3

The thickness of a hollow wooden cylinder is 3 cm. It is 35 cm long and its inner radius is 12 cm. Find the volume of the wood required to make the cylinder, assuming it is open at either end.

Right Option : C
View Explanation
Explanation
 
 
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