Volume of Spheres Examples

Find the volume of a sphere with a diameter of 20 millimeters.

If the diameter is 20 millimeters, the radius must be 10 millimeters.

All we need is the radius, and we're good to go.

V ≈ 4188.8 mm³

Fin.

Weebles wobble but they don't fall down. If Mr. Weebleton, the mayor of Weebletown, is 14 centimeters tall and has a radius of 4 centimeters, how big is he? All Weebles have this basic shape.

We can see that Mr. Weebleton looks like a cone and a hemisphere glued together. To calculate Mr. Weebleton's size, we can calculate the volumes of each solid. We'll start with the hemisphere, which is half the volume of a sphere.

V = ½(⁴⁄₃πr³)
V = ⅔π(4 cm)³
V ≈ 134 cm³

Halfway there. Remember that part of Mr. Weebleton's total height is due to the radius of the hemisphere. That means the height of the cone part of him is 10 centimeters, not 14. Or, you know, just look at the diagram.

V = ⅓πr²h

There's our cone volume formula. Substitute in our values. Yippee.

V = ⅓π(4 cm)²(10 cm)

V ≈ 167.6 cm³

All that's left is to add the two together. First grade stuff.

V_Weebleton = 134 cm³ + 167.6 cm³
V_Weebleton ≈ 301.6 cm³

Hopefully he doesn't think we're calling him fat.

If the diameter of the moon is 3476 kilometers, find its volume. If 1 km³ of cheese feeds 100 people and there are 8 billion people on Earth, could the moon feed the whole world? Assume that the moon is a perfect sphere, that it's made entirely of cheese, and that no one is lactose-intolerant.

By this point, we could find the radius from a diameter even when blindfolded with our hands tied behind our backs. The radius of the moon is 1738 kilometers. Just plug it into the formula.

V ≈ 21,990,642,871 km³

If each cubic kilometer of cheese feeds 100 people, we can convert cheese to people. That's a weird sentence.

21,990,642,871 km³ × 100 people/km³ = 2,199,064,287,100 people

The moon could feed nearly 2.2 trillion people. That means it could feed all 8 billion people in the entire world not once or twice, but about 275 times. Dig in, world.