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Question

Rachel, an engineering student, was asked to make a model shaped like a cylinder with two cones attached at its two ends by using a thin aluminium sheet. The diameter of the model is 3 cm and its length is 12 cm. If each cone has a height of 2 cm, find the volume of air contained in the model that Rachel made . (Assume the outer and inner dimensions of the model to be nearly the same.)


A

50 cm3

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B

66 cm3

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C

62 cm3

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D

75 cm3

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Solution

The correct option is B

66 cm3


Diameter of Cylinder = Diameter of Cones = 3 cm

Radius of Cylinder = Radius of Cones =r=32=1.5 cm

Height of each cone =h1=2 cm


Length of model = 12 cm

Height of Cylinder, h
= Total Height of Model - height of 1st Cone - height of 2nd Cone
=1222=8 cm

Volume of air in the model
= Volume of Solid
= Volume of Cylinder + Volume of 1st Cone + Volume of 2nd Cone

We know that, volume of a cylinder of radius r and height h is πr2h and volume of a cone of radius R and height H is given by 13πR2H.

Therefore, volume of air in the model
=πr2h+13πr2h1+13πr2h1

=πr2(h+h13+h13)

=227×1.5×1.5(8+43)

=227×1.5×1.5(283)=66 cm3


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