Question

(b) A cylinder of cross-sectional area 0.65m2 and

height 0.32m has a mass of 2. Ikg. If there is a
cavity inside, find the volume of the cavity.
(Density of cylinder = 11.053 kg/m^3)​

Answer 1

The volume of the cavity is 0.013m^3

Step-by-step explanation:

To find the volume of the cavity, the major parameter missing is the diameter of the cavity itself. we can obtain this using the following steps:

Step one:

Obtain the volume of the cylinder by dividing the mass of the cylinder by the density.

Volume of the cylinder = 2.1 / 11.053 =0.19
`m^(3)`

Step two:

From the volume of the cylinder, we can get the radius of the cylinder.

`radius = \sqrt{(V)/(\pi * h)} = \sqrt{(0.19)/(\pi * 0.32)} =0.44m`

Step three:

From the cross-sectional area, we can obtain the radius of the cavity.

Let the radius of the cavity be = r, while the radius of the cylinder be = R

CSA of cavity =

`\pi({R^2}-r^2) = CSA\\0.65 = \pi (0.32^2-r^2)\\r= 0.115m`

Step Four:

calculate the volume of the cavity using volume =
`\pi r^2 * h`

Recall that the cavity has the same height as the original cylinder

`volume = \pi * 0.115^2* 0.32= 0.013m^3`