QuestionScott weighs 335 lbs and has 6.3 qt of blood. If blood density is $1.21 \mathrm{~g} / \mathrm{mL}$ , find his blood mass in kg.

Studdy Solution

STEP 1

Assumptions1. Scott's blood volume is6.3 qt. The density of blood is $1.21 \mathrm{~g} / \mathrm{m}$ 3.1 quart =946 milliliters4. We want to find the mass of Scott's blood in kilograms

STEP 2

First, we need to convert the blood volume from quarts to milliliters. We can do this by multiplying the blood volume by the conversion factor.
$Blood\, volume\, in\, mL = Blood\, volume\, in\, qt \\times Conversion\, factor$

STEP 3

Now, plug in the given values for the blood volume and conversion factor to calculate the blood volume in milliliters.
$Blood\, volume\, in\, mL =6.3\, qt \\times946\, mL/qt$

STEP 4

Calculate the blood volume in milliliters.
$Blood\, volume\, in\, mL =6.3\, qt \\times946\, mL/qt =596.8\, mL$

STEP 5

Now that we have the blood volume in milliliters, we can find the mass of the blood. We can do this by multiplying the blood volume by the density of blood.
$Mass\, of\, blood\, in\, g = Blood\, volume\, in\, mL \\times Density\, of\, blood$

STEP 6

Plug in the values for the blood volume and the density of blood to calculate the mass of the blood.
$Mass\, of\, blood\, in\, g =5965.8\, mL \\times1.21\, g/mL$

STEP 7

Calculate the mass of the blood in grams.
$Mass\, of\, blood\, in\, g =5965.\, mL \\times1.21\, g/mL =7217.618\, g$

STEP 8

Now that we have the mass of the blood in grams, we need to convert this to kilograms. We can do this by dividing the mass in grams by1000, since there are1000 grams in a kilogram.
$Mass\, of\, blood\, in\, kg = Mass\, of\, blood\, in\, g /1000$

STEP 9

Plug in the value for the mass of the blood in grams to calculate the mass in kilograms.
$Mass\, of\, blood\, in\, kg =7217.618\, g /100$

STEP 10

Calculate the mass of the blood in kilograms.
$Mass\, of\, blood\, in\, kg =7217.618\, g /1000 =7.218\, kg$ The mass of Scott's blood is7.218 kg.

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