Question

a beverage company wanted to design a new line of canned drinks where each can is 12 centimeters tall with a volume of approximately 300 cubic centimeters. what should the diameter of the can be? use the formula for the volume of a cylinder, ( v=pi r^{2} h ), to find the diameter. use 3.14 for ( pi ) and round your answer to the nearest tenth, if necessary. use the keypad to enter the answer in the box. the diameter of the can should be about ( h=\frac{v}{pi r^{2}} ) centimeters.

Explanation:

Step1: Solve for \( r^{2} \)

Given \( V=\pi r^{2}h \), substitute \( V = 300\), \(h=12\), and \(\pi = 3.14\).

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Step2: Solve for \( r \)

Take the square - root of \( r^{2}\approx7.96\).

$$r=\sqrt{7.96}\approx 2.82$$

Step3: Solve for \( d \)

Since \(d = 2r\), substitute \(r\approx2.82\).

$$d=2\times2.82 = 5.64\approx5.6$$

Answer:

\(5.6\)