Question

the table below lists the masses and volumes of several pieces of the same type of metal. there is a proportional relationship between the mass and the volume of the pieces of metal.

volume (cubic centimeters)	mass (grams)
13.2	44.484
13.6	45.832

determine the mass, in grams, of a piece of metal that has a volume of 8.2 cubic centimeters. round your answer to the nearest tenth of a gram.

Explanation:

Step1: Find the constant of proportionality

Since there is a proportional relationship between mass $m$ and volume $V$, the constant of proportionality $k=\frac{m}{V}$. Using the first - row data: $k = \frac{43.136}{12.8}=3.37$.

Step2: Calculate the mass for a given volume

We know that $m = kV$. Given $V = 8.2$ cubic centimeters and $k = 3.37$, then $m=3.37\times8.2 = 27.634$.

Step3: Round the result

Rounding $27.634$ to the nearest tenth gives $27.6$.

Answer:

$27.6$