Question

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. type your answer in the box. b. the mass is 125 grams and the volume is v cubic centimeters. type your answer in the box. c. the volume is 1.4 cubic centimeters and the density is 80 grams per cubic centimeter. type your answer in the box. d. the mass is m grams and the volume is v cubic centimeters. type your answer in the box.

Explanation:

Step1: Recall density formula

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

Step2: Solve part a

Given $m = 500$ grams and $V=40$ cm³, substituting into the formula gives $D=\frac{500}{40}$.

Step3: Solve part b

Given $m = 125$ grams and $V = v$ cm³, the density formula gives $D=\frac{125}{v}$.

Step4: Solve part c

We know $D = 80$ g/cm³ and $V=1.4$ cm³. From $D=\frac{m}{V}$, we can rewrite it as $m=D\times V$. So $m = 80\times1.4$.

Step5: Solve part d

Given $m$ grams and $v$ cm³, by the density formula $D=\frac{m}{v}$.

Answer:

a. $D=\frac{500}{40}$
b. $D=\frac{125}{v}$
c. $m = 80\times1.4$
d. $D=\frac{m}{v}$