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= (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)= (4)/(3) \pi r^(3)`

radius (r)=
`(diameter)/(2)`=
`(8.0 mm)/(2) = 4.0 mm`

let's plug in the values

V=
`(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 ((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