Questions: Take a look at this sketch, and then answer the questions below about the mass, volume and density of Objects D D C neither (they are the same) unknown (can't be decided with this sketch) ----------------------------------------------------------------------------------- Which object has the greater mass? 0 0 0 Which object has the greater volume? 0 0 Which object has the greater density? 0 0 0

Take a look at this sketch, and then answer the questions below about the mass, volume and density of Objects D

D C neither (they are the same) unknown (can't be decided with this sketch)
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Which object has the greater mass? 0 0 0
Which object has the greater volume? 0 0
Which object has the greater density? 0 0 0

Transcript text: Take a look at this sketch, and then answer the questions below about the mass, volume and density of Objects $D$ 0 \begin{tabular}{|l|c|c|c|c|c|} \cline { 2 - 6 } \multicolumn{1}{l|}{} & D & C & \begin{tabular}{l} neither (they \\ are the same) \end{tabular} & \begin{tabular}{l} unknown (can't be \\ decided with this sketch) \end{tabular} \\ \hline \begin{tabular}{l} Which object has \\ the greater mass? \end{tabular} & 0 & 0 & & 0 \\ \hline \begin{tabular}{l} Which object has \\ the greater volume? \end{tabular} & 0 & 0 & & \\ \hline \begin{tabular}{l} Which object has \\ the greater density? \end{tabular} & 0 & 0 & & 0 \\ \hline \end{tabular}

Solution

Solution Steps

Step 1: Analyze the balance scale

The balance scale is balanced, meaning the total mass on each side is equal. On the left side, we have object D. On the right side, we have two identical objects, C. Therefore, the mass of D is equal to the mass of 2C. This means object D has a greater mass than a single object C.

Step 2: Analyze the volume

From the image, we can visually compare the volumes. Object D appears larger than a single object C. However, we cannot definitively say whether D is larger than two C objects combined. We don't have enough information to determine which object has a greater volume.

Step 3: Analyze the density

Density is mass divided by volume. We know that mass(D) = 2 * mass(C). Let's represent the mass of D as $m_D$ and the mass of C as $m_C$, and their volumes as $V_D$ and $V_C$ respectively. We have $m_D = 2m_C$. The density of D is $\rho_D = \frac{m_D}{V_D}$ and the density of C is $\rho_C = \frac{m_C}{V_C}$. We want to compare $\rho_D$ and $\rho_C$. Substituting $m_D = 2m_C$, we get $\rho_D = \frac{2m_C}{V_D}$. If $V_D = 2V_C$, then $\rho_D = \frac{2m_C}{2V_C} = \frac{m_C}{V_C} = \rho_C$, meaning they have the same density. If $V_D > 2V_C$, then $\rho_D < \rho_C$, meaning C has the greater density. If $V_D < 2V_C$, then $\rho_D > \rho_C$, meaning D has the greater density. Since we don't know the relationship between $V_D$ and $2V_C$, we cannot determine which object has a greater density.