Question

draw two fully worked - out ideas for the cup. include exact dimensions and the placement of the cold pack compartment. use text boxes to explain the ideas, and show the measurements. the total volume of the cup must be 750 cubic centimeters. the drink compartment must be 600 cubic centimeters to hold a 20 - ounce drink. the cold pack compartment must be 150 cubic centimeters (the volume of the reactants in the chemical reaction from task 1). you may want to review how to calculate the volume of a cylinder or rectangular prism.

Explanation:

Step1: Consider cylinder - idea 1

Let the drink compartment (cylinder) have volume formula $V=\pi r^{2}h$. Given $V = 600$ $cm^{3}$. Assume $h = 10$ $cm$, then $\pi r^{2}h=600$, so $\pi r^{2}\times10 = 600$, and $r^{2}=\frac{60}{\pi}$, $r=\sqrt{\frac{60}{\pi}}\approx4.37$ $cm$. For the cold - pack compartment (rectangular prism), assume it is a cube with volume $V = 150$ $cm^{3}$, then side length $a=\sqrt[3]{150}\approx5.31$ $cm$. Place the cube - shaped cold - pack beside the cylinder.

Step2: Consider rectangular prism - idea 2

For the drink compartment (rectangular prism), let length $l = 10$ $cm$, width $w=6$ $cm$, height $h = 10$ $cm$, then volume $V=l\times w\times h=10\times6\times10 = 600$ $cm^{3}$. For the cold - pack compartment (rectangular prism), let length $l_1 = 5$ $cm$, width $w_1=5$ $cm$, height $h_1 = 6$ $cm$, then volume $V_1=l_1\times w_1\times h_1=5\times5\times6 = 150$ $cm^{3}$. Place the cold - pack compartment on top of the drink compartment.

Answer:

Idea 1: Drink compartment is a cylinder with $r\approx4.37$ $cm$ and $h = 10$ $cm$, cold - pack is a cube with side length $\approx5.31$ $cm$ placed beside the cylinder. Idea 2: Drink compartment is a rectangular prism with $l = 10$ $cm$, $w = 6$ $cm$, $h = 10$ $cm$, cold - pack is a rectangular prism with $l_1 = 5$ $cm$, $w_1=5$ $cm$, $h_1 = 6$ $cm$ placed on top of the drink compartment.