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 two methods for coming up with your answer.

Explanation:

Method 1: Ratio - Proportion

Step1: Set up the proportion

Since the two cans are similar, the ratio of their diameters is equal to the ratio of their heights. Let the height of the mini - can be $h$. The proportion is $\frac{d_1}{d_2}=\frac{h_1}{h_2}$, where $d_1 = 6.25$ cm (diameter of standard can), $d_2 = 4$ cm (diameter of mini - can), $h_1 = 12.25$ cm (height of standard can), and $h_2$ is the height of the mini - can.
$\frac{6.25}{4}=\frac{12.25}{h}$

Step2: Cross - multiply and solve for $h$

Cross - multiplying gives $6.25h=4\times12.25$.
$6.25h = 49$.
Then $h=\frac{49}{6.25}=7.84$ cm.

Method 2: Scale Factor

Step1: Find the scale factor of the diameters

The scale factor $k$ from the standard can to the mini - can for the diameters is $k=\frac{d_{mini}}{d_{standard}}=\frac{4}{6.25}=\frac{16}{25}$.

Step2: Find the height of the mini - can

Since the cans are similar, the height of the mini - can is found by multiplying the height of the standard can by the scale factor.
$h = 12.25\times\frac{16}{25}=\frac{12.25\times16}{25}=\frac{196}{25}=7.84$ cm.

Answer:

The height of the new can is 7.84 cm.