How Do You Calculate the Mass of an Osmium Sphere?

[Mootiek]

I am having trouble with how to set up the equation for this problem...

Os is the densest element known. Given that the density of Os is 22.57g/cm^3, calculate the mass, in kg, of an Os sphere 15 cm in diameter, which is about the size of a grapefruit.

Any help would be greatly appreciated. I am really confused with where the diameter fits in... I feel so lost in this class! Yikes!

 

[morrobay]

You need to work on the basics:
Volume of a sphere = 4/3( pi ) (radius cubed)
Density = mass/volume

 

[Blueshift5]

Hello there,

I understand that you are having trouble with calculating the mass of an Os (osmium) sphere and setting up the equation for this problem. I will try my best to explain it to you.

First, let's review the information given in the problem. It states that Os is the densest element known, with a density of 22.57g/cm^3. This means that for every 1 cm^3 of Os, it weighs 22.57 grams.

Next, we need to consider the size of the sphere. It is given that the sphere has a diameter of 15 cm, which is about the size of a grapefruit. This diameter is important because it helps us determine the volume of the sphere.

The formula for calculating the volume of a sphere is V = (4/3)πr^3, where r is the radius of the sphere. In this case, the diameter is given, so we can find the radius by dividing it by 2. Therefore, the radius is 7.5 cm.

Now, let's plug in the values into the formula for volume: V = (4/3)π(7.5 cm)^3 = 1767.15 cm^3. This means that the sphere has a volume of 1767.15 cm^3.

To find the mass of the sphere, we can use the formula for density, which is mass divided by volume (d = m/V). Since we want to find the mass, we can rearrange the formula to m = d x V.

Substituting the values, we get m = (22.57 g/cm^3) x (1767.15 cm^3) = 39846.65 g. This is the mass of the sphere in grams.

To convert it to kilograms, we need to divide it by 1000, since there are 1000 grams in 1 kilogram. Therefore, the mass of the Os sphere is 39.84665 kg.

I hope this helps you understand how to set up the equation and solve this problem. Just remember to always pay attention to the units and use the correct formulas. If you have any further questions, don't hesitate to ask for help. Good luck with your studies!