Chapter 6.2, Problem 30WE

To determine

To calculate: The volume of the cube with edgelength $\frac{4n}{5}\text{ in}$.

Answer to Problem 30WE

The volume of the cubeis $\frac{64n^3}{125}\text{ in}$.

Explanation of Solution

Given information:

A cube with edge length of $\frac{4n}{5}\text{ in}$.

Formula used:

Volume $\left(V\right)$ of cube is third power of its edge. Let edge of the cube be of length $\left(l\right)$ . It is mathematically denoted by $V=l^3$.

Law of exponent for a quotient raised to power m where m is a positive integer is ${\left(\frac{a}{b}\right)}^m=\frac{a^m}{b^m}$.

Law of exponent for a product of two terms raised to power m where m is a positive integer is ${\left(ab\right)}^m=a^m{b}^m$.

Calculation:

Consider the provided statement a cube with edgelength $\frac{4n}{5}\text{ in}$.

Recall that volume $\left(V\right)$ of cube is cube of its edge. Let edge of the cube be of length $\left(l\right)$ . It is mathematically denoted by $V=l^3$ . Recall that law of exponent for a quotient raised to power m where m is a positive integer is ${\left(\frac{a}{b}\right)}^m=\frac{a^m}{b^m}$ and law of exponent for a product of two terms raised to power m where m is a positive integer is ${\left(ab\right)}^m=a^m{b}^m$.

Apply it,

  $\begin{array}{c}V=l^3\\ ={\left(\frac{4n}{5}\text{ in}\right)}^3\\ =\frac{{\left(4n\right)}^3}{5^3}{\text{ in}}^3\\ =\frac{64n^3}{125}{\text{in}}^3\end{array}$

Thus, the volume of the cubeis $\frac{64n^3}{125}\text{ in}$.