Question

Solve for $h$ in $V = \dfrac{1}{3}\pi {r^2}h$ ?

Answer 1

Hint:The value of h in $V = \dfrac{1}{3}\pi {r^2}h$ can be found by using the method of transposition. Method of transposition involves doing the exact same mathematical thing on both sides of an equation with the aim of simplification in mind. This method can be used to solve various algebraic equations like the one given in question with ease.

Complete step by step answer:
We would use the method of transposition to find the value of h in $V = \dfrac{1}{3}\pi {r^2}h$. Method of transposition involves doing the exact same thing on both sides of an equation with the aim of bringing like terms together and isolating the variable or the unknown term in order to simplify the equation and finding the value of the required parameter.

Now, In order to find the value of h, we need to isolate h from the rest of the parameters such as r and $\pi $.
So, $V = \dfrac{1}{3}\pi {r^2}h$
Dividing both sides by $\dfrac{{\pi {r^2}}}{3}$, we get,
$ \Rightarrow $\[\dfrac{V}{{\left( {\dfrac{{\pi {r^2}}}{3}} \right)}} = \dfrac{{\dfrac{1}{3}\pi {r^2}h}}{{\left( {\dfrac{{\pi {r^2}}}{3}} \right)}}\]

Now, cancelling the common terms in the numerator and denominator, we get,
$ \Rightarrow $\[\dfrac{V}{{\left( {\dfrac{{\pi {r^2}}}{3}} \right)}} = h\]
Simplifying the left side of equation as the variable h is isolated in the right side of the equation,
$ \Rightarrow $\[\dfrac{{3V}}{{\pi {r^2}}} = h\]
So, changing the sides of equation, we get,
$ \therefore $\[h = \dfrac{{3V}}{{\pi {r^2}}}\]

Hence, the value of h in $V = \dfrac{1}{3}\pi {r^2}h$ is \[\dfrac{{3V}}{{\pi {r^2}}}\].

Note: If we add, subtract, multiply or divide by the same number on both sides of a given algebraic equation, then both sides will remain equal. The given problem deals with algebraic equations and can be easily solved by dividing both sides by $\dfrac{{\pi {r^2}}}{3}$. There is no fixed way of solving a given algebraic equation. Algebraic equations can be solved in various ways. Linear equations in one variable can be solved by a transposition method with ease.