Question

a spherical sample has a mass of 2.813g. it has a diameter of 8.0mm. what is the sphere made of (determined by its density as g/cm *3)

Answer 1

to determine the density, we use the following formula:

$density= \frac{mass}{volume}$

mass= 2.813 grams
volume= ?

we need to first calculate the volume before we can solve for the density. since the question states that the sample has a spherical shape, we can use the volume formula of spheres to find it.

$Sphere_{volume}= \frac{4}{3} \pi r^{3}$

radius (r)= $\frac{diameter}{2}$= $\frac{8.0 mm}{2} = 4.0 mm$

let's plug in the values

V= $\frac{4}{3} \pi 4^{3} = 268 mm^3$

we need to change the $mm^3$ to $cm^3$ using the following conversion

1 cm= 10 mm
$268 mm^3 (\frac{1 cm}{10 mm} )^3 = 0.268 cm^3$

now we can find the density. 

density= 2.813 grams/ 0.268 cm= 10.5 g/cm3