How can I calculate density of a solid?

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Answer 1 · 2014-05-16T20:13:23

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

$D = \frac{m a s s}{v o l u m e} or D = \frac{m}{V}$ $D = (mass)/(volume) or D = m/V$

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

$D = \frac{m}{V} or D V = m or V = \frac{m}{D}$ $D = m/V or DV = m or V =m/D$

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 $l x h x w$ $l x h x w$
$6.0 c m x 0.5 c m x 2.0 c m = 6.0 c m^{3}$ $6.0 cm x 0.5 cm x 2.0 cm = 6.0 cm^3$

Now the density is $\frac{m a s s}{v o l u m e}$ $(mass)/(volume)$

$D = \frac{42 g}{6.0 c m^{3}}$ $D = (42 g)/(6.0 cm^3)$

$D = 7.0 \frac{g}{c m^{3}}$ $D = 7.0 g/(cm^3)$

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 $l x h x w$ $l x h x w$
$6.0 c m x 0.5 c m x 2.0 c m = 6.0 c m^{3}$ $6.0 cm x 0.5 cm x 2.0 cm = 6.0 cm^3$

Now the density is $\frac{m a s s}{v o l u m e}$ $(mass)/(volume)$

$D = \frac{42 g}{6.0 c m^{3}}$ $D = (42 g)/(6.0 cm^3)$

$D = 7.0 \frac{g}{c m^{3}}$ $D = 7.0 g/(cm^3)$

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 $(3.14) r^{2} h$ $(3.14) r^2h$
$(3.14) {(2 c m)}^{2} (3.0 c m) = 37.68 c m^{3}$ $(3.14) (2cm)^2(3.0cm) = 37.68 cm^3$

Now the density is $\frac{m a s s}{v o l u m e}$ $(mass)/(volume)$

$D = \frac{33.0 g}{37.68 c m^{3}}$ $D = (33.0 g)/(37.68 cm^3)$

$D = 0.876 \frac{g}{c m^{3}}$ $D = 0.876 g/(cm^3)$

I hope this was helpful.
SMARTERTEACHER

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