Question

Osmium (Os) is the densest element known (density =22.57 g/cm^3). Calculate the mass in pounds and in kilograms of an Os sphere 15 cm in diameter (about the size of a grapefruit) (volume of a sphere of radius r is 4/3Ïr^3).

Answer 1

Answer: The mass of osmium in kilograms and in pounds are 318.9141 kg and 703.085 pounds.

Explanation:

To calculate the volume of sphere, we use the formula:

$V=\frac{4}{3}\pi r^3$

where,

r = radius of sphere

We are given:

Radius of osmium = 15 cm

Volume of osmium = $\frac{4}{3}\times 3.14\times (15)^3=14130cm^3$

Density of osmium = $22.57g/cm^3$

To calculate mass of a substance, we use the equation:

$Density=\frac{Mass}{Volume}$

Putting values in above equation, we get:

$22.57g/cm^3=\frac{\text{Mass of osmium}}{14130cm^3}\\\\\text{Mass of osmium}=318914.g$

To convert the given mass into kilo grams and pounds, we use the conversion factors:

1 kg = 1000 grams

So, $318914.1g=318914.1g\times \frac{1kg}{1000g}=318.9141kg$

And,

1 pound = 453.592 g

So, $318914.1g=318914.1g\times \frac{1pound}{453.592g}=703.085pounds$

Hence, the mass of osmium in kilograms and in pounds are 318.9141 kg and 703.085 pounds.