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.

Step-by-step explanation:

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

`V=(4)/(3)\pi r^3`

where,

r = radius of sphere

We are given:

Radius of osmium = 15 cm

Volume of osmium =
`(4)/(3)* 3.14* (15)^3=14130cm^3`

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

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

`Density=(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* (1kg)/(1000g)=318.9141kg`

And,

1 pound = 453.592 g

So,
`318914.1g=318914.1g* (1pound)/(453.592g)=703.085pounds`

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