Question

1. a standard coke can has a diameter of 6.25 centimeters and a height of 12.25 centimeters. coca - cola is considering launching a coca - cola mini can with a diameter of 4 centimeters. what would the height of the new can be if the two cans are similar? show your work.

Explanation:

Step1: Set up the proportion

For similar - shaped cylinders (Coca - Cola cans), the ratio of their diameters is equal to the ratio of their heights. Let the height of the new can be $h$. The ratio of diameters is $\frac{d_1}{d_2}$, and the ratio of heights is $\frac{h_1}{h_2}$. We know that $d_1 = 6.25$ cm, $h_1 = 12.25$ cm, and $d_2 = 4$ cm. The proportion is $\frac{d_1}{d_2}=\frac{h_1}{h_2}$.

Step2: Substitute the values into the proportion

Substituting the given values into the proportion $\frac{6.25}{4}=\frac{12.25}{h}$.

Step3: Cross - multiply

Cross - multiplying gives us $6.25h=4\times12.25$.

Step4: Solve for $h$

First, calculate $4\times12.25 = 49$. Then, $h=\frac{49}{6.25}=\frac{49}{\frac{25}{4}}=49\times\frac{4}{25}=\frac{196}{25}=7.84$ cm.

Answer:

$7.84$ cm