Question

The volume of a cube is 125x^3y^3 cubic units, and the area of its base is 25x^2y^2 square units. What is the length of an edge of the cube in units,if x > 0 and y> 0?

Answer 1

By formula the volume of a cube is given as;

`\begin{gathered} \text{V = BA}* H \\ \text{Where V=volume} \\ BA=\text{base area =area of square = L}* L \\ H=\text{height = length of the edge} \\ L=\text{length of the base shape.} \end{gathered}`
`\begin{gathered} \text{where V=125x}^3y^3 \\ BA=L^2=25x^2y^2 \\ H=\text{ ?} \end{gathered}`

Substituting these values into the formula above, we get

`\begin{gathered} 125x^3y^3=25x^2y^2H \\ \text{Dividing both sides by 25x}^2y^2\text{ , we get} \\ H=(125x^3y^3)/(25x^2y^2)=5xy \\ H=5xy\text{ units} \end{gathered}`

Hence, the correct answer is 5xy units.