Question

part 2 of 2
mental math an engineer makes different - size samples of a new material. the table shows volumes and the related masses. what would be the mass of 100 cubic centimeters of the material? of 500 cubic centimeters of the material? use pencil and paper. explain how you can use mental math to find the answer
the mass of 100 cubic centimeters of the material would be 1000 grams.
the mass of 500 cubic centimeters of the material would be grams

Explanation:

Step1: Find the unit rate

From the table, when \(x = 9\), \(y=90\). The unit rate (density) \(k=\frac{y}{x}\). So \(k = \frac{90}{9}=10\) grams per cubic - centimeter.

Step2: Calculate the mass for \(x = 100\)

Using the formula \(y=kx\), when \(x = 100\) and \(k = 10\), then \(y=10\times100 = 1000\) grams.

Step3: Calculate the mass for \(x = 500\)

Using the formula \(y=kx\), when \(x = 500\) and \(k = 10\), then \(y=10\times500=5000\) grams.

Answer:

The mass of 500 cubic centimeters of the material would be \(5000\) grams.