Question

What is the volume of a hollow cylinder with radius r, wall thickness d (d < r) and length L? (Hint: use Eq. (1.2) twice). What would be the mass of the sphere in the previous question if it were hollow with uniform wall thickness of 3 cm?

Equation (1.2) Volume of the Sphere =

Answer 1

a)

A hollow cylinder's volume will be the difference of volume of a solid cylinder with radius r and a solid cyclinder of radius d, where d < r, i.e., subtracting volume a solid cylinder of radius d from a solid cylinder of radius r will given us the remaining volume.

Volume of solid cylinder with radius r : Vr

Volume of solid cylinder with radius d: Vd

Hence, Volume of remaining hollow cylinder : V = Vr - Vh

b)

We can apply the same principle of hollow cylinder with sphere as well. Given that the thickness of sphere wall is 3 cm. Lets assume that the radius of outside solid sphere with this 3 cm (or 0.03 m) thickness included is r.

So, Volume of outside solid sphere : Vo

Also, Volume of inside solid sphere : Vi

Hence, Volume of hollow sphere : V = Vo - Vi

Also, Mass = Density * Volume

Lets say the density is rho, then:

where V is the volume stated above.

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