Question

You have $10$ gallons of lemonade to sell. $(1\mathrm{gal}\approx 3785{\mathrm{cm}}^3)$

Each customers uses $1$paper cup.

The cups are sold in packages of $50$.

How man packages should you buy?

Answer 1

Step 1: Given

$$\begin{gathered} \mathrm{Height}\mathrm{of}\mathrm{cup}=11\mathrm{cm} \\ \mathrm{Radius}\mathrm{of}\mathrm{cup}=\frac{8}{2}=4\mathrm{cm} \end{gathered}$$

Step 2: Volume of one cup $=\frac{1}{3}$ Bh Write the formula for volume

$$\begin{gathered} =\frac{1}{3}\mathrm{\pi }{\left(4\right)}^2\left(11\right)\mathrm{Substitute} \\ =\frac{176}{3}\mathrm{\pi } \\ =184.30\mathrm{cubic}\mathrm{cm} \\ \mathrm{Total}\mathrm{volume}\mathrm{of}\mathrm{lenonade}=3785*10=37850{\mathrm{cm}}^3 \end{gathered}$$

Step 3:

$$\begin{gathered} \mathrm{Number}\mathrm{of}\mathrm{cups}\mathrm{required}=\frac{37850}{184.30}=205.37=205\mathrm{cups}\mathrm{approx} \\ \mathrm{Number}\mathrm{of}\mathrm{packets}\mathrm{required}=\frac{205}{50}=4.1=5\mathrm{packets} \end{gathered}$$

Final Answer: Number of packets required = 5 packets