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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.
Solution
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
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