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.)  [use `pi = 22/7`]

Answer 1

From the figure, it can be observed that

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 = Radius of conical part  = `3/2` cm

Volume of air present in the model = Volume of cylinder + 2 × Volume of cones

= `pir^2h_2 + 2xx1/3pir^2h_1`

= `22/7(3/2)^2(8)+2xx1/3pi(3/2)^2 (2)`

= `22/7xx9/4xx8+2/3pixx9/4xx2` cm³

= `22/7 xx 9/4 xx ((24 + 4)/3)` cm³

= `(22/7 xx 9/4 xx 28/3)` cm³

= 66 cm³