Q13. - Algebra 1

Question

A cylindrical container of chocolate drink mix has a volume of about$\mathbf{162}\mathit{i}{\mathit{n}}^{\mathbf{3}}$. The radius of the container can be found by using the formula$\mathit{r}\mathbf{=}\sqrt{\frac{\mathbf{V}}{\mathbf{\pi }\mathbf{h}}}$, where$\mathit{r}$is the radius and$\mathit{h}$ is the height. If the height is$\mathbf{8}\mathbf{.}\mathbf{25}$inches, find the radius of the cylinder.

Step-by-Step Solution

Answer

The radius of the cylinder is $\mathbf{2}\mathbf{.}\mathbf{5}$ inches.

Step 1. State the concept of ‘Volume of cylinder’.

The volume of a cylinder is the capacity of the cylinder which tells the amount of material it that can be immersed in it.

Suppose $‘r’$ is the radius and $‘h’$ is the height of the cylinder, then the volume of the cylinder  $\left(V\right)$ is given as:

 $V=\pi r^{2}h$

Step 2. State the concept of ‘principle square root’.

Every real numbers have two square roots, one positive and one negative. The non-negative (positive) square root is called the Principal square Root. Principal square root is denoted as $\sqrt{}$.

Step 3. Calculate the radius.

Substitute $V=162$ and $h=8.25$ in $r=\sqrt{\frac{V}{\pi h}}$ to get the required value.

$\begin{array}{c}r=\sqrt{\frac{V}{\pi h}}\\ =\sqrt{\frac{162}{\pi \times 8.25}}\\ =\sqrt{\frac{162}{25.918}}\\ =\sqrt{6.250}\\ =\sqrt{6.25}\\ =2.5\end{array}$

Therefore, the radius of the cylindrical container is $2.5$ inches.