A cylindrical tube 10.9 cm high and 2.20 cm in diameter is used to collect blood samples. How many cubic decimeters (dm3) of blood can it hold (V of a cylinder = πr2h)?

Question

Answer in the correct number of significant figures.

Answer 1

Hello, Dawson,

Take the dimension values, enter them in a table, and then use the formula to calculate the volume:

We've found the volume, but the question want it expressed in dm³, [Who uses decimeter these days?].

We need to convert cm³ to dm³.

Start with the definition of dm. 1 dm = 10 cm.

Make this into a conversion factor by dividing both sides by 10cm: 1dm/10cm = 1

Since the value (1dm/10cm) = 1, we can multiply it times anything and still have a valid number, but one that has new units;

Since we need cm³, lets take the same equation and raise both sides to the third power:

1dm³/(1000cm³) = 1³ [= 1]

Now we can multiply this times the 41.4cm³:

(41.4cm³)*(1dm³/(1000cm³)

Note how the units for cm³ cancel, leaving just dm³.

(41.4cm³)*(1dm³/(1000cm³)= 41.4dm³/1000 = 41.4dm³/10³

The answer is 4.14 x10^-2 dm³

3 sig figs is what we started with.

Bob