Sphere Formula

The subject of sphere formula encompasses a wide range of important elements. Question #c84c8 - Socratic. Explanation: To find the rate of increase of the radius, we need an expression that we can use which will result in a derivative of radius with respect to time. Since we are first given a rate of volume change of #40 (cm^3)/s#, it seems like a natural starting point to use the volume of a sphere formula. Moreover, either of two unit spheres passes through the center of the other ....

The two spherical surfaces meet along a small circle of radius sqrt3/2 units, with center as the midpoint of the line joining the centers of the spheres. Use the formula: The volume of a conical part of the unit sphere, with conical (semi- vertical) angle alpha radian and vertex at the center of the sphere = 4/3 alpha sin alpha cubic units. Can someone help me solve this problem? A=pi (r^2-h^2) If we let hatr be the radius of the circular cross-section (as opposed to simple r, the radius of the sphere, then by the Pythagorean Theorem color (white) ("XXX") (hatr)^2=r^2-h^2 The Area of the circular cross-section is given by the standard formula for the area of a circle: color (white) ("XXX")A=pi * (hatr)^2 color (white) ("XXX"A)=pi * (r^2-h^2)

Spherical coordinates are (rho, theta, phi). In relation to this, and x = rho sin phi cos ⁡ theta, y = rho sin phi cos ⁡ theta, z = rho cos ⁡ phi and rho^2=x^2+y^2+z^2 with further restrictions rho ∈ [0, ∞), phi ∈ [0, π) The limits for the variables in the given problem are 0<=x<=sqrt(4-y^2) 0<=y<=2 sqrt(x^2+y^2)<=z<=sqrt(8-x^2-y^2) Considering only the = sign of equality, the ... Explanation: The volume of sphere is given by the formula #V_s= 4/3pir^3#; Thevolume of cone is given by the formula #V_c=h/3pir^2#. The condition here is that #V# and #r# of both figures are equal. By equating the two formulas, the following can be derived: Questions asked by Sidharth - Socratic.

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Simplify: (help me please)? Volume of a sphere is given by V=4/3πr³ , where r is its radius . If radius changes by 1.2% , then find the change in the volume ? This perspective suggests that, perimeter of rectangle? How do you use Pascal's triangle to determine the first four terms of the expanded expression # (x+y)^4#?

Answers created by Dean R. Site Map - Distance Formula Questions and Videos | Socratic. Questions What is the Distance Formula? In this context, how can the distance formula be derived from the pythagorean theorem? How can the distance formula be used in real life?

How do you find the distance when given two coordinate points? How do you find the distance between (7, 7) and (–7, 7)? Given an organic formula #C_ (n)H_ (m)N_ (l)O_ (p)# how ...