Question

How do you solve for $B$: $V=Bh$?

Answer 1

Hint: We first explain the terms in the equation $V=Bh$. We find the particular three-dimensional figures which follow the formula. We find their volume and base area. From the values we verify the result.

Complete step by step solution:
The given equation $V=Bh$ is the formula to find the volume of some particular three-dimensional figures.
In the equation three variables have been used. These variables have their own meaning for the figure. The variable $V$ stands for the volume of the figure. The variable $B$ stands for the area of the base of the figure. The variable $h$ stands for the height of the figure.
The three-dimensional figures which satisfy the formula are prism, cube, cuboid, cylinder.
All three variables are just numbers. We can treat them as algebraic variables.

For example: in the case of a cube the base area is $B={{x}^{2}}$ where $x$ is the side length of the cube. Then the volume is $V=Bh={{x}^{2}}\times x={{x}^{3}}$. Here the height of the cube is also x.
Therefore, we can just divide both sides of the equation $V=Bh$ with $h$.
The equation becomes
$
 \Rightarrow V=Bh \\
 \Rightarrow \dfrac{V}{h}=\dfrac{Bh}{h}=B \\
$
Therefore, the solution for $B$ from the equation $V=Bh$ is $B=\dfrac{V}{h}$.
We verify the result from the perspective of the cube. Base was $B={{x}^{2}}$. We verify the result with
$B=\dfrac{V}{h}=\dfrac{{{x}^{3}}}{x}={{x}^{2}}$.
Thus verified $B$ is $B=\dfrac{V}{h}$.

Note: We can only solve this equation in cases where the volume follows the formula. In cases where the formula changes the value of $B$ also changes according to the formula. We need to remember that the equation does not necessarily have to be a formula for volume all the time.