Question

Water is being poured into a "Dixie cup" (a standard cup that is smaller at the bottom

Answer 1

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

$\displaystyle V=\frac{\pi r^2h}{3}$

This function relates the height with the volume, to find the required function, let's solve for h

$\displaystyle h=\frac{3V}{\pi r^2}$

Rearranging

$\displaystyle h=\frac{3}{\pi r^2}\cdot V$

Being all the values positive, the height and the volume are linearly related with positive slope

Answer: (c) a straight line with positive slope.