Answer :
To determine how many kilograms of calcium are present in a 165-pound man, given that 1.4% of the mass of a human body is calcium, follow these steps:
1. Convert the man's weight from pounds to kilograms:
The conversion factor from pounds to kilograms is approximately 0.453592 kg per pound.
[tex]\[
165 \ \text{pounds} \times 0.453592 \ \frac{\text{kg}}{\text{pound}} = 74.84268 \ \text{kg}
\][/tex]
2. Calculate the mass of calcium in the body:
Since 1.4% of the body mass is calcium, multiply the total body mass by 0.014.
[tex]\[
74.84268 \ \text{kg} \times 0.014 = 1.04779752 \ \text{kg}
\][/tex]
So, there are approximately [tex]\(1.048 \ \text{kilograms}\)[/tex] of calcium in a 165-pound man.
Now, look at the given options to find the best match for this result:
- [tex]\(5.1 \times 10^2 \ \text{kg Ca}\)[/tex]: This is 510 kg, which is far too high.
- 5.1 kg Ca: This is too high.
- 1.0 kg Ca: This is close to our calculation.
- [tex]\(1.0 \times 10^2 \ \text{kg Ca}\)[/tex]: This is 100 kg, which is far too high.
Therefore, the closest and correct answer is:
1.0 kg Ca.
1. Convert the man's weight from pounds to kilograms:
The conversion factor from pounds to kilograms is approximately 0.453592 kg per pound.
[tex]\[
165 \ \text{pounds} \times 0.453592 \ \frac{\text{kg}}{\text{pound}} = 74.84268 \ \text{kg}
\][/tex]
2. Calculate the mass of calcium in the body:
Since 1.4% of the body mass is calcium, multiply the total body mass by 0.014.
[tex]\[
74.84268 \ \text{kg} \times 0.014 = 1.04779752 \ \text{kg}
\][/tex]
So, there are approximately [tex]\(1.048 \ \text{kilograms}\)[/tex] of calcium in a 165-pound man.
Now, look at the given options to find the best match for this result:
- [tex]\(5.1 \times 10^2 \ \text{kg Ca}\)[/tex]: This is 510 kg, which is far too high.
- 5.1 kg Ca: This is too high.
- 1.0 kg Ca: This is close to our calculation.
- [tex]\(1.0 \times 10^2 \ \text{kg Ca}\)[/tex]: This is 100 kg, which is far too high.
Therefore, the closest and correct answer is:
1.0 kg Ca.
