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

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.

Accepted Answer

Step 1: Radius of each cone $=$ Radius of cylinder $= \frac{3}{2}$ cm. Height of each cone $H = 2$ cm.
Step 2: Height of cylinder $h = 12 - 2 - 2 = 8$ cm
Step 3: Volume of air $= \pi r^2 h + 2 	imes \frac{1}{3} \pi r^2 H = \pi r^2 \left(h + \frac{2H}{3}ight)$
Step 4: $= \frac{22}{7} 	imes \frac{9}{4} 	imes \left(8 + \frac{4}{3}ight) = \frac{22}{7} 	imes \frac{9}{4} 	imes \frac{28}{3} = 66$ cm$^3$

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