Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [spheres]

For geometrical problems involving spheres. Use the tag (geometry) as well. For intrinsic geometry of spheres, see (spherical-geometry).

An $n$-sphere is $$ S^n = \{\mathbf x \in \mathbb{R}^{n+1}\mid \lVert x \rVert_2 = 1\} $$ Its enclosed volume is the $(n+1)$-ball.

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Find the surface area of the circumcyclinder

The surface area of a sphere with radius $r$ is $4 \pi r^2 $. Find the surface area of its circumscribing cylinder. I don't know to begin the problem. I would highly value your hints
user366082
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Sphere Packing inside a quadratic space

How would you go about calculating the number of uniform spheres that could fit inside a given quadratic surface , say an elliptic paraboloid of a fixed height, given the radius of said spheres and the equation of the quadratic surface? Assuming…
pmaurais
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Conical frustum tangent to two spheres

I've two spheres in cartesian space: $(x_1, y_1, z_1, r_1)$ and $(x_2, y_2, z_2, r_2)$. They don't intersect each other. I want to calculate the conical frustum tangent to these two spheres. In particular, I need to find the center point and the…
Jepessen
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What shape does the intersection of two spheres yield? How do you find the center and radius of this circle?

Suppose I have two spheres of arbitrary size $S_1$ and $S_2$ and I intersect them so they overlapped some extent. What kind of shape would their intersection create? In other words, what does $S_1 \cap S_2$ look like? EDIT: Someone has suggested…
Stan Shunpike
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Calculating the mean square distance between two points on the sphere.

The Question What I want to know is how to calculate the mean square distance between a fixed point which is any random point in the sphere and rest of the points. My Understanding I'm clueless on how to calculate it. I'm a beginner. First I started…
Venus8588
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Find the sum of the volumes

Let $d$ be the distance between the centers of two spheres which are in contact with each other. Let $A$ be the sum of the surface areas of the two spheres. Find the sum of the volumes of the two spheres(in terms of $d$ and $A$).
Ryan Scott
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