Question

object a has a density of 2.0 $\frac{g}{cm^{3}}$ and a mass of 100 g. object b a density of 0.8 $\frac{g}{cm^{3}}$ and a mass of 240 g. object c a density of 5.0 $\frac{g}{cm^{3}}$ and a mass of 100 g. which of the objects above (a, b, or c) has the least volume? select the correct answer below: object a object b object c all of the objects have the same volume

Explanation:

Step1: Recall density formula

The density formula is $
ho=\frac{m}{V}$, where $
ho$ is density, $m$ is mass and $V$ is volume. We can re - arrange it to find volume $V = \frac{m}{
ho}$.

Step2: Calculate volume of Object A

Given $
ho_A=2.0\frac{g}{cm^3}$ and $m_A = 100g$. Using $V=\frac{m}{
ho}$, we have $V_A=\frac{m_A}{
ho_A}=\frac{100g}{2.0\frac{g}{cm^3}} = 50cm^3$.

Step3: Calculate volume of Object B

Given $
ho_B=0.8\frac{g}{cm^3}$ and $m_B = 240g$. Using $V=\frac{m}{
ho}$, we have $V_B=\frac{m_B}{
ho_B}=\frac{240g}{0.8\frac{g}{cm^3}}=300cm^3$.

Step4: Calculate volume of Object C

Given $
ho_C=5.0\frac{g}{cm^3}$ and $m_C = 100g$. Using $V=\frac{m}{
ho}$, we have $V_C=\frac{m_C}{
ho_C}=\frac{100g}{5.0\frac{g}{cm^3}} = 20cm^3$.

Step5: Compare volumes

We have $V_A = 50cm^3$, $V_B=300cm^3$ and $V_C = 20cm^3$. Since $20cm^3<50cm^3<300cm^3$, Object C has the least volume.

Answer:

C. Object C