# sphere

3. ### How do I find the velocity of a sphere falling when an observer riding an elevator?

The problem is as follows: In a certain shopping mall which is many stories high, there is a glass elevator in the middle plaza. One shopper riding the elevator notices a kid drops a spheric toy from the top of the building where is located the toy store. The shopper riding the elevator labeled...
4. ### Cube inside sphere

The largest cube that can fit into a sphere must have eight vertices touching the surface of the sphere. Express the side length, s, of the cube in terms of the diameter, D, of the sphere. Posted this in the elementary forum, but realised there was an algebra forum, anyway quick responses...
5. ### Axes of a complex sphere

The axes for a complex circle are real and imaginary. What is the other axis needed to construct a complex sphere?
6. ### Formula for this point distrubution on a sphere?

sphere A series of points are plotted on a unit radius sphere with its center at the origin of the coordinate system, see image. Points on XY and XZ planes (marked yellow) are created so that horizontal points coordinates in spherical system (r,fi,theta) are (1, n*A, 0) and vertical are (1, 0...
7. ### pressure gradient in sphere

Have cylinder made from semipermeable material .There is positive pressure inside cylinder and negative pressure outside cylinder .How gradient of pressure will be changed if we convert from cylinder t o sphere? Thank you
8. ### Area 1 circles on radius 1 sphere

What is the maximum number of circles of area one packable, without overlapping, onto a sphere of radius one? (I couldn't figure out StackExchange's use of tags.)
9. ### Pack unit circles on unit sphere

What is the maximum number of non-overlapping unit circles that can be packed upon a unit sphere?
10. ### Riemann Sphere

What is the connection between Riemann Sphere to Trigonometric Functions?
11. ### Interactive sphere eversion

I have put an interactive model of the deNeve/Hills sphere eversion at http://chrishills.org.uk/sphereeversion/interactive/. You can click-and-drag to change the viewpoint, drag the Zoom slider to change the zoom, and drag the AnimationSpeed slider to speed up and slow down the animation...
12. ### Proof of Surface Area and Volume of a sphere Using Integral Calculus

Hi! Letâ€™s consider a sphere with a radius r. What's his volume and his area. The full answer is given in the following link : https://smartmanmaths.com/2017/09/22/proof-of-surface-area-and-volume-of-a-sphere-using-integral-calculus/ Thanks and enjoy your mind!
13. ### Calculating a density of a sphere

An object occupies the region inside the unit sphere at the origin, and has density equal to the distance from the x-axis. Find the mass. This is my solution \int_{0}^{2 \pi} \int_{0}^{\pi} \int_{0}^{1} \sqrt{1-\rho^2 sin(\phi)^2 cos(\theta)^2} \rho^2 sin(\phi) d \rho d \phi d...
14. ### Quadrilaterals on a sphere

Does there exist a mapping of equivalent quadrilaterals that covers exclusively an entire spherical surface? Without two singularities?
15. ### Equation of sphere with spherical coordinates

Hello everyone, I am stuck on this problem where we are given a spherical coordinate equation and must find the cartesian equation. The cartesian equation represents a sphere and they want us to find the center and radius. I have my work attached and the problem written there. My plan of...
16. ### Sphere and Plane intersection

If \beta is the radius of the circle of intersection of the sphere x^2+y^2+z^2-2x-4y-6z+ \alpha=0 and the plane $x+y+z=1$, then the relation between \alpha and \beta is : A) 3 \alpha + 3 \beta^2 =17 B) 3 \alpha^2 - 3 \beta^2 =17 C) 3 \alpha^2 - 3 \beta^2 =67 D) 3 \alpha + 3...
17. ### Line Integral: intersection of sphere and cylinder

Vectorial Field: F(x, y, z) = (yÂ², zÂ², xÂ²) Sphere: xÂ² + yÂ² + zÂ² = aÂ² Cylinder: xÂ² + yÂ² = ax z<=0 ; a>0 How to parametrize the curve?? The exercise says it's clockwise when seen by the xy plan
18. ### Largest square on sphere

What is the largest square that can be constructed on a unit sphere?
19. ### Triple Integral of a sphere question

Compute âˆ« âˆ« âˆ« x + y + z dV over the region x^2 + y^2 + z^2 <= 1 in the First octant. Answer: 3pi/16 I would be much appreciated if anyone show me how to define the boundaries of this integral. Thanks.
20. ### Spheres within sphere packing

What is the maximum number of spheres of radius one that can be packed within a sphere of radius 3?