Question

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

Answer 1

Answer:

The volume of the cavity is 0.013m^3

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.

$radius = \sqrt{\frac{V}{\pi \times h}} = \sqrt{\frac{0.19}{\pi \times 0.32}} =0.44m$

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 =$\pi r^2 \times h$

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

$volume = \pi \times 0.115^2\times 0.32= 0.013m^3$