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.)
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
=12−2−2=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