Question

A student was asked to make a model shaped like a cylinder with two cones attached to its ends by using a thin aluminium sheet. The diameter of the model is 3 cm and its total length is 12 cm. If each cone has a height of 2 cm, find the volume of air contained in the model.

Answer 1

Given, height of each cone (h) = 2 cm

Total Length of model = 12 cm

Diameter of model = 3 cm

Now, Length of cylinder (H) = Total length of model – 2 × height of cone

= 12 – 2 × 2

= 12 – 4

= 8 cm

and radius of cone = radius of cylinder (s)

= `"Diameter of model"/2`

= `3/2` cm

Now, volume of the model = Volume of cylinder + 2 × Volume of cone

= πr²H + 2 × `1/3` πr²h

= πr²`("H" + 2/3)"h"`

= `22/7xx(3/2)^2xx(8+2/3xx2)`

= `22/7xx9/4xx(24+4)/3`

= `(3xx22xx28)/(7xx4)`

= 66 cm³