Question

The volume of a conical flask is V cubic centimeters. The height of the flask is the same as its radius. Which function can be used to find the radius of the flask given its volume, the table for f(x) or the graph of g(x)? Explain your answer. If needed, use the graphing tool to arrive at your conclusion.

Answer 1

Use an equation to determine whether f(x) or g(x) is the correct model. Create an equation for the radius of the flask in terms of its volume.

Because the height is the same as the radius, write this formula for the volume of the flask:

V=
`(1)/(3)`
`\pi r^(3)`

Rewrite the formula, solving for r:

`(3V)/(\pi ) =r^(3)`

`\sqrt[3]{(3V)/(\pi ) } =r`

Now, graph the function and try to identify the values that are in the table.

The graph of the function does match the table of values. So, the table for f(x) can be used to find the radius of the flask. Notice that the graph for g(x) doesn’t match the graph of the formula, so exclude it as the answer.

Explanation:

This is the sample answer for edmentum/plato so you should change it a bit.

Answer 2

Table for
`f(x)`.

Explanation:

The table offers a greater accuracy in comparison with graph, since any measure in the latter is subject to a margin of error associated with limitations of human sight, whereas any value can be either used directly from table, or estimated by linear interpolation on the assumption that curve is smooth, guaranteeing lower margins of error.