Chapter 12, Problem 9MCQ

To determine

To calculate:To find the amount of water to be added in the can

Answer to Problem 9MCQ

The amount of water to be added in the can is $111.3i{n}^3$

Explanation of Solution

Given information:A can of lemonade concentrate has a diameter of $3$ inches and a height of $4\frac{1}{2}$ inches. Also, the concentrate dissolves in $3\frac{1}{2}$ cans of water

Formula Used:

Volume of cylinder is given as

  $Volume=\pi r^{2}h$

Where,

  $r=$ Radius

  $h=$ Height

Calculation:

Given that a can of lemonade concentrate has a diameter of $3$ inches and a height of $4\frac{1}{2}$ inches.

Here, can is in shape of cylinder

Thus, Volume of can of lemonade is calculated as

  $Volume=\pi r^{2}h$

Substituting the values, volume is

  $\begin{array}{l}Volume=\pi {\left(\frac{3}{2}\right)}^2\times 4\frac{1}{2}\\ Volume=\frac{22}{7}\times \frac{3}{2}\times \frac{3}{2}\times \frac{9}{2}\\ Volume=\frac{11}{7}\times \frac{3}{2}\times \frac{3}{2}\times \frac{9}{1}\\ Volume=\frac{891}{28}\end{array}$

Also given that concentrate dissolve in $3\frac{1}{2}$ cans of water

Thus, amount of water is calculated as follows:

  $\begin{array}{l}Amount=3\frac{1}{2}\times \frac{891}{28}\\ Amount=\frac{7}{2}\times \frac{891}{28}\\ Amount=\frac{1}{2}\times \frac{891}{4}\\ Amount=\frac{891}{8}\\ Amount=111.3i{n}^3\end{array}$

Conclusion:

Hence, the amount of water to be added in the can is $111.3i{n}^3$