**Q) **A student was asked to make a model 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.

**Ans: **

We know that, volume of the cone = r^{2} h_{1}. Here, r is the radius of cylinder and h_{1} is the height of cylinder.

and the volume of the cylinder = r^{2} h_{2}. Here, r is the radius of cone and h_{2} is the height of cone.

*[Note: Since radius is same for given cylinder and both cones, we have taken same variable of r, but since heights are different for both shapes, we have taken different variables.]*

The volume of the model = volume of left cone + volume of the cylinder + volume of right cone

= r^{2 }h_{1} + r^{2} h_{2} + r^{2}h_{1}

= r^{2} ( h_{1} + h_{2} + h_{1})

= r^{2} ( h_{1} + h_{2})

It is given that the diameter of the model is 3 cm

the radius r = cm;

the height of cone h_{1} = 2 cm;

the height of the cylinder h_{2} = 12 – 2 – 2 = 8 cm

Hence, the volume of the model:

=

=

= 22 x 3 = 66 cm^{3}

**Therefore, the volume of the model is 66 cm ^{3}**