A standard baseball has a circumference of approximately 23cm. If a baseball has the same mass per unit volume as a neutron or a proton, about what would its mass be?

Some info:

Mass of Proton/Neutron: 10^-27 kg

Length of Proton/Neutron: 10^-15m (diameter)

I know I have to convert the diameter of the proton/neutron to its circumference, after that I'm not sure if I divide its mass to its length and then multiply by the circumference of the ball or not.

TY

## Answers (1)

The ball has a circumference of 23 cm, from that, you can get its radius. Divide the circumference by 2π, it should give you a radius of 3.66 cm. Now find the volume, you do that by plugging the radius into the equation V=4/3πr³. That comes down to 205.46 cm³ for the ball.

Now to find the density of the proton. First, we convert the diameter of the proton from m to cm. Then we divide the diameter by 2 to get the radius and use the same volume formula as above. That gives us an extremely tiny volume of 5.24x10^-40 cm³.

Then we find the density of the proton, the formula for which is D=M/V. So we take the given mass and volume and plug them in. That gives us an extremely LARGE density of 1.91x10^12 kg/cm³.

Then we take the volume of the baseball we found earlier and use the newly found density to gauge its mass. We reformat the density equation into DV=M. This gives us a ball that weighs... 392,399,695,300,000 kilograms. Yikes...

Just goes to show that protons are very dense things.