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.)​

Answer 1

Volume of Air Contained in Model

= Volume of Model

= Volume of Cylinder + Volume of 1st cone + Volume of 2nd Cone

= πr²h + 1/3πr²h + 1/3πr²h

= (π × r² × h) + (1/3 × π × r² × h) + (1/3 × π × r² × h)

= (22/7 × (3/2)² × h) + (1/3 × 22/7 × (3/2)² × h) + (1/3 × 22/7 × (3/2)² × h)

= (22/7 × 9/4 × h) + (1/3 × 22/7 × 9/4 × 2) + (1/3 × 22/7 × 9/4 × h)

= (198/28 × h) + (22/217 × 9/4 × h) + (22/21 × 9/4 × h)

= (198/28 × (12 - 4)) + (22/21 × 9/4 × 2) + (22/21 × 9/4 × 2)

= (198/28 × 8) + (22/21 × 9/4 × 2) + (22/21 × 9/4 × 2)

= (198/28 × 8) + (22/21 × 9/2 × 1) + (22/21 × 9/2 × 1)

= (198/28 × 8) + (22/21 × 9/2) +  (22/21 × 9/2)

= (1584/28) + (198/42) + (198/42)

= (56.57) + (4.71)  + (4.71)

= 65.99 cm³

≈ 66 cm³