# How can I calculate density of a solid?

May 16, 2014

Density is a comparison of the mass of an object and the volume of that object.

$D = \frac{m a s s}{v o l u m e} \mathmr{and} D = \frac{m}{V}$

This equation can be rearranged algebraically to solve foray of the values.

$D = \frac{m}{V} \mathmr{and} D V = m \mathmr{and} V = \frac{m}{D}$

Let us look at two sample problems.

A rectangular prism has a mass of 42.0 grams and has dimensions of 2 cm in width, 6 cm long and 0.5 cm in height. What is the density of this object?

Volume of a rectangular prism is $l x h x w$
$6.0 c m x 0.5 c m x 2.0 c m = 6.0 c {m}^{3}$

Now the density is $\frac{m a s s}{v o l u m e}$

$D = \frac{42 g}{6.0 c {m}^{3}}$

$D = 7.0 \frac{g}{c {m}^{3}}$

A rectangular prism has a mass of 42.0 grams and has dimensions of 2 cm in width, 6 cm long and 0.5 cm in height. What is the density of this object?

Volume of a rectangular prism is $l x h x w$
$6.0 c m x 0.5 c m x 2.0 c m = 6.0 c {m}^{3}$

Now the density is $\frac{m a s s}{v o l u m e}$

$D = \frac{42 g}{6.0 c {m}^{3}}$

$D = 7.0 \frac{g}{c {m}^{3}}$

A cylinder has a mass of 33.0 grams and has a diameter of 4 cm and measure 3.0 cm in height. What is the density of the cylinder?

Volume of a cylinder is $\left(3.14\right) {r}^{2} h$
$\left(3.14\right) {\left(2 c m\right)}^{2} \left(3.0 c m\right) = 37.68 c {m}^{3}$

Now the density is $\frac{m a s s}{v o l u m e}$

$D = \frac{33.0 g}{37.68 c {m}^{3}}$

$D = 0.876 \frac{g}{c {m}^{3}}$ 