Q12 of 44 Page 14

A student was asked to make a model in his workshop, which shaped like a cylinder with two cones attached at its two ends, using a thin aluminium sheet. The diameter of the model is 3 cm and its length is 10 cm. If each cone has a height of 2cm, find the volume of air contained in the model. (Consider the outer and inner dimensions of the model to be nearly the same).


Given that diameter of cylinder = 3cm


So,


Given: Height of cone = 2cm


and


Height of the cylinder + height of cone + height of cone = 10cm


Height of the cylinder + 2 + 2 = 10


Height of the cylinder = 6cm


So,


Volume of the cylinder = πr2h



= 42.428 cm3


= 42.43 cm3 (approx.)




= 4.71 cm3


Volume of 1st cone = Volume of 2nd cone = 4.71cm3


So, Total volume of the model


= Volume of cylinder + volume of 1st cone + volume of 2nd cone


= 42.43 + 4.71 + 4.71


= 51.85cm3


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