Answer:
(c) a straight line with positive slope.
Step-by-step explanation:
Functions
We are required to find a function that relates the height of the water in a cup to the volume of water in the cup.
The cup has a shape of a cone open upwards. The volume of a cone of height h and radius r is
[tex]\displaystyle V=\frac{\pi r^2h}{3}[/tex]
This function relates the height with the volume, to find the required function, let's solve for h
[tex]\displaystyle h=\frac{3V}{\pi r^2}[/tex]
Rearranging
[tex]\displaystyle h=\frac{3}{\pi r^2}\cdot V[/tex]
Being all the values positive, the height and the volume are linearly related with positive slope
Answer: (c) a straight line with positive slope.
