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.
We know that, volume of the cone = r2 h1. Here, r is the radius of cylinder and h1 is the height of cylinder.
and the volume of the cylinder = r2 h2. Here, r is the radius of cone and h2 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
= r2 h1 + r2 h2 + r2h1
= r2 ( h1 + h2 + h1)
= r2 ( h1 + h2)
It is given that the diameter of the model is 3 cm
the radius r = cm;
the height of cone h1 = 2 cm;
the height of the cylinder h2 = 12 – 2 – 2 = 8 cm
Hence, the volume of the model:
= 22 x 3 = 66 cm3
Therefore, the volume of the model is 66 cm3