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

They have same density

Step-by-step explanation:

The density of an object is defined as

`d=(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 = (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 = (V_c)/(3)`

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

`m_d = (m_c)/(3)`

So, the density of ball D is:

`v_d = (m_d)/(V_d)=(m_c/3)/(V_d/3)=(m_c)/(V_c)=d_c`

Therefore, the two balls have same density.