During surgery, a patient receives 3.0 pt of blood. How many kilograms of blood (density = 1.06 g/mL) were needed for the transfusion?

To calculate how many kilograms of blood were needed for the transfusion, we will first convert the volume of blood from pints (pt) to milliliters (mL), then use the density to find the mass, and finally convert the mass from grams to kilograms.

### Step 1: Convert pints to milliliters
We know that:
- 1 pint = 473.176 mL

So, for 3.0 pints of blood:
\[
3.0 \, \text{pt} \times 473.176 \, \frac{\text{mL}}{\text{pt}} = 1419.528 \, \text{mL}
\]

### Step 2: Use the density to find the mass of the blood
The density of blood is given as 1.06 g/mL. The mass \( m \) of the blood can be calculated using the formula:
\[
\text{mass} = \text{density} \times \text{volume}
\]
\[
m = 1.06 \, \frac{\text{g}}{\text{mL}} \times 1419.528 \, \text{mL} = 1504.7 \, \text{g}
\]

### Step 3: Convert grams to kilograms
Since 1 kilogram = 1000 grams:
\[
\text{mass in kilograms} = \frac{1504.7 \, \text{g}}{1000} = 1.5047 \, \text{kg}
\]

### Final Answer:
The patient needed approximately **1.50 kilograms of blood** for the transfusion.

Would you like further details or have any questions?

Here are 5 related questions for further exploration:
1. How would the mass change if the density of blood was different?
2. How does the density of other fluids in the body compare to blood?
3. What other units could the mass of blood be measured in?
4. How does blood volume relate to body weight?
5. How would this calculation change if the volume was given in liters?

**Tip**: When converting units, always double-check conversion factors for accuracy, especially when switching between different systems (e.g., metric and imperial).

Determine the mass of blood in kilograms needed for a transfusion based on a volume of 3.0 pints and a density of 1.06 g/mL. This step-by-step guide covers unit conversion, density application, and metric calculations, suitable for high school students in Grades 9-12.

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