Question

Find the volume of a 4-dimensional sphere with radius 4.

Answer 1

What do you mean by volume? Note that the term surface area is used for 3-dimensional objects.

Answer 2

I just have a problem that asks for the volume of a 4-dimensional sphere.

Answer 3

Okay, I'll assume that it's asking for the 4-D measurement of the 4-D object

Answer 4

Is this for calculus?

Answer 5

no, it was from a math contest. I know the answer but I want to figure out how you get it.

Answer 6

I would take the equation of the sphere
f(x,y,z) = x^2 + y^2 + z^2
And triple integrate it.

Answer 7

https://en.wikipedia.org/wiki/N-sphere

Answer 8

https://upload.wikimedia.org/wikipedia/commons/5/59/N_SpheresVolumeAndSurfaceArea.png

Answer 9

ok, I think I understand it now. Thanks!

Answer 10

No problem