Question

How do you solve for $b$ in $V=\dfrac{1}{3}bh$ ?

Answer 1

Hint:Here in this question we have been asked to solve the given expression $V=\dfrac{1}{3}bh$ for $V$ . For answering this question, we will perform a simple transfer from left hand side to right hand side and vice-versa.

Complete step-by-step answer:
Now considering from the question we have been asked to solve the given expression $V=\dfrac{1}{3}bh$ for $V$ .
For answering this question, we will perform a simple transfer from left hand side to right hand side and vice-versa.
Firstly we will transfer $h$ from right hand side to left hand side. After doing that we will have \[V\left( \dfrac{1}{h} \right)=\dfrac{1}{3}b\] .
Now we will transfer $\dfrac{1}{3}$ from right hand side to left hand side. After doing that we will have \[V\left( \dfrac{1}{h} \right)\left( 3 \right)=b\] .
Now we can write this expression simply as $\dfrac{3V}{h}=b$ .
Therefore we can conclude that the solution for $b$ in the given expression $V=\dfrac{1}{3}bh$ will be given as $b=\dfrac{3V}{h}$ .

Note: While answering this type of questions we have to be sure with the simplifications that we are going to perform in between the steps in order to answer them. This is a very simple and easy question and can be answered accurately within a short span of time. Very few mistakes are possible in this type of question. Alternatively this question can be answered by considering the simplification as
$\begin{align}
  & V=\dfrac{1}{3}bh\Rightarrow \left( \dfrac{1}{b} \right)V=\dfrac{1}{3}h \\
 & \Rightarrow \dfrac{1}{b}=\dfrac{1}{3}h\left( \dfrac{1}{V} \right)\Rightarrow b=\dfrac{3V}{h} \\
\end{align}$
We have ended up having the same conclusion as before.