Question

The formula for the volume of a cylinder is $V=\pi {{r}^{2}}h$, where $\pi =\dfrac{22}{7}$. Find r, when h = 14 and V = 396.

Answer 1

Hint: In this question, we will find the height of the cylinder using the formula $V=\pi {{r}^{2}}h$. We already know the volume and height as it is given in the question and we have to find the unknown variable i.e. r. So, by directly substituting the given V and h values in the formula, we will be able to find the radius of the cylinder.

Complete step-by-step answer:
We know that volume of a cylinder is given by $V=\pi {{r}^{2}}h$, where r = radius of the cylinder, h = the height of the cylinder and $\pi $ is a constant and its value is $\dfrac{22}{7}$. Let us consider the figure as below,

We know that according to the question value of h is 14 and the value of V is 396. Now, we will find r using the formula $V=\pi {{r}^{2}}h$.
Now we will substitute V and h values in the above formula, and get,
$\Rightarrow 396=\pi \times ({{r}^{2}})\times 14.........(1)$
We will take the value of $\pi =\dfrac{22}{7}$ as mentioned above. Now, we will substitute the value in equation (1). Then, we will get
$\Rightarrow 396=\dfrac{22}{7}\times ({{r}^{2}})\times 14$
Now we will cancel 14 with 7 as 14 is a multiple of 7 and it will yield 2 as shown below,
$\Rightarrow 396=22\times ({{r}^{2}})\times 2$
On further simplification, i.e. multiplying 22 with 2, we will get
$\Rightarrow 396=44\times ({{r}^{2}})$
Now we will divide both sides with 44 and we will get,
$\Rightarrow 9={{r}^{2}}$
Now taking the square on both sides, we will get $r= \pm \sqrt{9}\Rightarrow r=\pm 3$. Now, since the radius cannot be negative, we will take only the positive value. Therefore, we will take $r=3$.
Hence, we have found the value of the radius as 3.

Note: Here the value of $\pi $ is given as $\dfrac{22}{7}$. If not specified, we must take the value as $\dfrac{22}{7}$ only and proceed to do the problem. The height is a multiple of 7, hence $\pi =\dfrac{22}{7}$ will make the calculations easier. We must be careful while doing calculations while finding a variable. If we make a small mistake during calculations, it will affect the final answer.