Multiple Dimensions - Surface Area Of A 4-Sphere

Calculus Level 2

What is the surface area of the sphere of radius $r$ in 4 dimensions?

2 \pi r^3

2 \pi^2 r^3

\pi^2 r^3

\pi r^3

1 solution

Himanshu Parihar
May 16, 2014

from previous problem if we diffrentiate the volume we get the answer.

Actually, there is a faster way.

The volume of a n-dimensional pyramid with height h and "base area" b has volume (1/n)(b)(h).

So the volume of the 4-D sphere is basically (1/4)(surface area)(r)

So surface area = 4(volume)(1/r) = 4*(1/2)(pi^2)(r^4)(1/r) = 2(pi^2)(r^3)

Aloysius Ng - 5 years, 2 months ago