If the VOLUME of a rectangular prism is $945 cm ^{3}$, then what is the value of the length $X$ of the base?
To find the length of the base of the rectangular prism, we need to use the formula for the volume of a rectangular prism, which is:
Volume = length x width x height
Given that the volume is $945 cm^3, we can set up the equation as:
$945 = X \times Y \times Z$
Since we are looking for the value of the length $X$, we need to express the width and height in terms of $X$. Let's say the width of the base is $Y$ and the height is $Z$. Therefore, the equation becomes:
$945 = X \times Y \times Z$
We know that $X \times Y$ is the area of the base, which is equal to $X \times Y = X^2$, so the equation simplifies to:
$945 = X^2 \times Z$
Given that the volume is $945 cm^3, we can calculate the value of $Z$ by dividing the volume by the area of the base, which is $945 / X^2$. Therefore, the equation becomes:
$945 = X^2 \times \dfrac{945}{X^2}$
Solving this equation will give us the value of $X$, the length of the base.