Cylinder mug with 3 cm radius & 10 cm height, density of sugar in cylinder= .01(10-h) what is the mass of sugr

Question

Cylinder mug with 3 cm radius & 10 cm height, density of sugar in cylinder= .01(10-h) what is the mass of sugr

Answer 1

This is an odd question, as the density of the sugar is changing with respect to the height.  This does happen to a certain degree, but definitely not to the degree shown by this equation.

Nevertheless, all we need to do is find the average density throughout the 10cm height.

Note: I will assume that the density formula given above gives density in g/cm^3, since no units are provided.

The density at the bottom of the cylinder is:

0.01(10-0) = 0.1 g/cm^3

Th density at the top of the cylinder is:

0.01(10-10) = 0 g/cm^3

The average density throughout the cylinder will now be:

0.5(0.1 + 0) = 0.05 g/cm^3

Next we need to determine the total volume of the sugar in the mug.  Taking the dimensions as the inner dimensions of the mug (to ignore the thickness of the mug) we get:

V = L(pi)(r^2)

V = 10(pi)(3^2)

V = 282.74 cm^3

Thus the total mass of the sugar will be:

0.05 g/cm^3 (282.74 cm^3) = 14.1 g