Question

The density of osmium is 22.57 g/cm^3. If a 1.00 kg rectangular block of osmium has two dimensions of 4.00 cm x 4.00 cm, calculate the third dimension of the block.

Answer 1

Well, density is mass divided by volume. So as of now, we can say we have this equation:
\[22.57g=\frac{ 1000g }{ V } \]The reason I put 1000g is because I want the units to be the same, so I said 1kg is the same as 1000g. So now I can solve for V by multiply both sides by V first to get:
\[V22.57g = 1000g\]And now by dividing both sides by 22.57, giving me a volume of:
\[V = \frac{ 1000g }{ 22.57g }\approx 44.31\]So now we can use this figure to get our missing dimension.
As you know, volume would be length x width x depth. We are given two dimensions already being 4.00cm and 4.00cm. So if the total volume is 44.31, we can say set up this equation to solve for the 3rd dimension:
\[(4.00)(4.00)x = 44.31\]So now we just solve for x. 4 times 4 is just 16, so we have:
\[16.00x = 44.31\]Now we divide both sides by 16 to get the 3rd dimension:

\[x = \frac{ 44.31 }{ 16 }\approx 2.77cm. \]