Question: In 2D, a sphere can be described by.In 3D, a sphere can be described by.We can talk about a sphere in-dimensions by defining it like.

In 2D, a sphere can be described by.In 3D, a sphere can be described by.We can talk about a sphere in-dimensions by defining it like.

Using what we know about multivariable calculus, believe it or not, it is relatively easy to calculate the volume of an-dimensional sphere. It turns out that the volume of a 5th dimensional sphere of radius 1 will be a maximum, and then the volume of 6th, 7th, 8th, etc. dimensional spheres will be less. In fact, as the dimension increases, the volume gets closer and closer to 0.

Explore and expand upon this idea by calculating the surface area of spheres inn -dimensions.

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