Question

The volume (v) of a sphere varies directly as the cube of its diameter (d). Write this statement in algebraic language, using an equation with the variables c, v, and d.

Answer 1

`\bf \qquad \qquad \textit{direct proportional variation}\\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------\\\\ \stackrel{\textit{volume}}{v}=\stackrel{\textit{constant of variation}}{c}\cdot \stackrel{\textit{cube of diameter}}{d^3}\implies v=cd^3`

Answer 2

Answer:
`v=cd^3`

Explanation:

The equation for direct variation between x and y (dependent variable) is given by :-

`y=kx`, where k is the proportionality constant.

Let the algebraic expression for the volume of sphere is v and for diameter is d.

The given statement : The volume of a sphere varies directly as the cube of its diameter.

Then the algebraic equation for the given statement will be :-

`v=cd^3`, where c is the proportionality constant.