A spherical object has a radius of 28.9 cm. If the density of the object is 3.52 g/cm^3, what is its mass?

Sep 13, 2017

$\text{Mass} = 355.9$ $\text{kg}$

Explanation:

First, let's find the volume of the spherical object.

The formula for the volume of a sphere is:

$R i g h t a r r o w V = \frac{4}{3} \pi {r}^{3}$

$R i g h t a r r o w V = \frac{4}{3} \cdot \pi \cdot {28.9}^{3}$ ${\text{cm}}^{3}$

$R i g h t a r r o w V = \frac{4 \pi}{3} \cdot 24 , 137.6$ ${\text{cm}}^{3}$

$\therefore V = 101 , 107.2$ ${\text{cm}}^{3}$

Then, let's find the mass of the spherical object.

The formula for density is:

Rightarrow "Density" = frac("mass")("volume")

Let's express it in terms of $\text{mass}$:

$R i g h t a r r o w \text{Mass" = "density}$ $\cdot$ $\text{volume}$

$R i g h t a r r o w \text{Mass} = 3.52$ ${\text{g/cm}}^{3}$ $\cdot$ $101 , 107.2$ ${\text{cm}}^{3}$

$R i g h t a r r o w \text{Mass} = 355 , 897.3$ $\text{g}$

$R i g h t a r r o w \text{Mass} = 355 , 897.3 \times {10}^{- 3}$ $\text{kg}$

$\therefore \text{Mass} = 355.9$ $\text{kg}$