Question

If ball C is 3 times the volume of ball D and ball D has 1/3 the mass of ball C, which has the greater density?

Answer 1

Answer:

They have same density

Explanation:

The density of an object is defined as

$d=\frac{m}{V}$

where

m is the mass of the object

V is its volume

Let's call $m_c$ and $V_c$ the mass and the volume of ball C, respectively. Therefore, the density of ball C is:

$d_c = \frac{m_c}{V_c}$

We know that the volume of ball C is 3 times the volume of ball D, so

$V_c = 3 V_d \rightarrow V_d = \frac{V_c}{3}$

And we also know that ball D has 1/3 the mass of ball C:

$m_d = \frac{m_c}{3}$

So, the density of ball D is:

$v_d = \frac{m_d}{V_d}=\frac{m_c/3}{V_d/3}=\frac{m_c}{V_c}=d_c$

Therefore, the two balls have same density.