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 aluminum 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)
Height (h1) of each conical part = 2 cm
Height (h2) of cylindrical part = 12 - 2 × Height of conical part
= 12 - 2 ×2
= 8 cm
Radius (r) of cylindrical part =
cm
Radius of conical part =
cm
Volume of air present in the model = Volume of cylinder + 2 × Volume of cones
= πr2h2 + 2 * 
r2h1
= π (
)2 (8) 2 * 
(
)2 (2)
= 18π + 3π
= 21π
= 66cm2
Hence, volume of air contained in the model that Rachel made = 66cm2