Question

9 from unit 2, lesson 2 the density of an object can be found by taking its mass and dividing by its volume. write an equation to represent the relationship between the three quantities (density, mass, and volume) in each situation. let the density, d, be measured in grams/cubic centimeters (or g/cm³). a. the mass is 500 grams and the volume is 40 cubic centimeters. b. the mass is 125 grams and the volume is v cubic centimeters. c. the volume is 1.4 cubic centimeters and the density is 80 grams per cubic centimeter. d. the mass is m grams and the volume is v cubic centimeters. + learning targets + i can use words and equations to describe the patterns i see in a table of values or in a set of calculations. + when given a description of a situation, i can use representations like diagrams and tables to help make sense of the situation and write equations for it.

Explanation:

Step1: Recall density formula

The formula for density is $D=\frac{m}{V}$, where $D$ is density, $m$ is mass and $V$ is volume.

Step2: Solve part a

Given $m = 500$ grams and $V=40$ $cm^{3}$, substituting into the formula $D=\frac{m}{V}$, we get $D=\frac{500}{40}=12.5$ $g/cm^{3}$.

Step3: Solve part b

Given $m = 125$ grams and $V = v$ $cm^{3}$, the density formula gives $D=\frac{125}{v}$ $g/cm^{3}$.

Step4: Solve part c

Since $D=\frac{m}{V}$, we can rewrite it as $m = D\times V$. Given $V = 1.4$ $cm^{3}$ and $D = 80$ $g/cm^{3}$, then $m=80\times1.4 = 112$ grams.

Step5: Solve part d

Given $m$ grams and $V = v$ $cm^{3}$, using the density formula $D=\frac{m}{v}$ $g/cm^{3}$.

Answer:

a. $D = 12.5$ $g/cm^{3}$
b. $D=\frac{125}{v}$ $g/cm^{3}$
c. $m = 112$ grams
d. $D=\frac{m}{v}$ $g/cm^{3}$