Question

How do you solve the formula for h in the surface area of a cylinder : $S=2\pi {{r}^{2}}+\pi rh$ ?

Answer 1

Hint: Here we have the equation $S=2\pi {{r}^{2}}+\pi rh$ where $r$ is the radius of the cylinder and $h$ is the height of the cylinder. Whenever we have such each equation , all we have to do is make use of basic mathematics which is transferring all the wanted variables to the opposite side of the wanted variable and make the entire equation as a function of the wanted variable.

Complete step by step answer:
For example , we have, $s=ax+b$ and I want to find $x$ from this equation. We have $s=ax+b$ . We will transfer my $b$ and $a$ to the other side which has $s$ . We get the following :
$\Rightarrow \dfrac{s-b}{a}=x$ . Now this became a function of $x$ and we got my $x$ .
In the same way , we find out $h$ from $S=2\pi {{r}^{2}}+\pi rh$.
First let’s transfer $2\pi {{r}^{2}}$ to the left hand side which has $S$ . Upon doing so, we get the following :
$\Rightarrow S-2\pi {{r}^{2}}=\pi rh$
Now let’s also transfer $\pi $ and $r$ . Upon doing so , we get the following :
$\Rightarrow \dfrac{S-2\pi {{r}^{2}}}{\pi r}=h$
$\Rightarrow \dfrac{S}{\pi r}-\dfrac{2\pi {{r}^{2}}}{\pi r}=h$
$\Rightarrow \dfrac{S}{\pi r}-2r=h$
Now we got a function of h in terms or variable $r$ and constant $\pi $. S is the surface area of the cylinder. It changes if the values of $h$ and $r$ changes. So it depends on both $h,r$ . It is a function of them.

$\therefore $ Hence $h=\dfrac{S}{\pi r}-2r$ from the formula $S=2\pi {{r}^{2}}+\pi rh$

Note: We have to be careful while transferring the unwanted variables to the opposite side. We just be alert and check which variable is asked for and then make it the subject. Make the entire equation as the function of the asked variable. We should be careful with the $+,-$ symbols as they may lead to calculation errors.