Question

graph the radical equation that can be used to calculate the radius, r, of the tank. use the lowercase
\ and the uppercase \v\ when entering the equation. after the equation has been entered, set the value of pi to be 3.14.

Explanation:

Step1: Recall Volume Formula

Assume the tank is a sphere (common for radius - volume relation). Volume of a sphere: \( V=\frac{4}{3}\pi r^{3} \). Solve for \( r \):
\( r^{3}=\frac{3V}{4\pi} \), so \( r = \sqrt[3]{\frac{3V}{4\pi}} \).

Step2: Substitute \( \pi = 3.14 \)

\( r=\sqrt[3]{\frac{3V}{4\times3.14}}=\sqrt[3]{\frac{3V}{12.56}} \).
To graph, we can consider \( V \) as the independent variable (x - axis) and \( r \) as the dependent variable (y - axis). For example, if \( V = 12.56 \), \( r=\sqrt[3]{\frac{3\times12.56}{12.56}}=\sqrt[3]{3}\approx1.44 \). Plot points by choosing \( V \) values, calculating \( r \), and graphing the cube - root function.

Answer:

The radical equation for \( r \) (assuming spherical tank) is \( r=\sqrt[3]{\frac{3V}{4\pi}} \) (or \( r=\sqrt[3]{\frac{3V}{12.56}} \) with \( \pi = 3.14 \)), and it can be graphed as a cube - root function.