What is the cross section of a sphere?
Any cross-section of the sphere is a circle. The vertical cross-section of a cone is a triangle, and the horizontal cross-section is a circle. The vertical cross-section of a cylinder is a rectangle, and the horizontal cross-section is a circle.
How do you write an equation for spherical coordinates?
To convert a point from spherical coordinates to cylindrical coordinates, use equations r=ρsinφ,θ=θ, and z=ρcosφ. To convert a point from cylindrical coordinates to spherical coordinates, use equations ρ=√r2+z2,θ=θ, and φ=arccos(z√r2+z2).
How do you find the dS of a sphere?
On the surface of the sphere, ρ = a, so the coordinates are just the two angles φ and θ. The area element dS is most easily found using the volume element: dV = ρ2 sin φ dρ dφ dθ = dS · dρ = area · thickness so that dividing by the thickness dρ and setting ρ = a, we get (9) dS = a2 sin φ dφ dθ.
What is equation of sphere?
Answer: The equation of a sphere in standard form is x2 + y2 + z2 = r2. Let us see how is it derived. Explanation: Let A (a, b, c) be a fixed point in the space, r be a positive real number and P (x, y, z ) be a moving point such that AP = r is a constant.
What is cross section formula?
In order to calculate the area of a cross-section, you need to look at them as basic shapes. For instance, a tube is a concentric circle. Therefore, for a tube with inner and outer diameter ( d and D ) having thickness t , the area of cross-section can be written as: AC = π * (D2 – d2) / 4.
How do you find cross sections?
A cross section is the shape we get when cutting straight through an object. The cross section of this object is a triangle. It is like a view into the inside of something made by cutting through it. This is a cross-section of a piece of celery.
What is Z in spherical coordinates?
z=ρcosφr=ρsinφ z = ρ cos φ r = ρ sin and these are exactly the formulas that we were looking for. So, given a point in spherical coordinates the cylindrical coordinates of the point will be, r=ρsinφθ=θz=ρcosφ r = ρ sin φ θ = θ z = ρ cos
What is a formula for a sphere?
The formula for the volume of a sphere is V = 4/3 πr³.
What is the formula of perimeter of sphere?
The Circumference of a circle or a sphere is equal to 6.2832 times the Radius. The Circumference of a circle or a sphere is equal to 3.1416 times the Diameter.
How many coordinates are necessary to determine a sphere?
If you mean determine any (blank) sphere, then you will need four coordinates: three to determine the center of the sphere and one to determine the radius. Let’s assume the whole space is the sphere so the centre is the origin. Assume a unit sphere. Then two coordiates for the rotation?
What is the general equation of spheres?
The general equation of the sphere is x2 + y2 + z2 = r2 and in this article, we will learn about deriving the equation of a sphere along with its volume and surface area. Deriving the Equation of A Sphere For a circle, whose center lies at the origin (0,0), the equation is given by: x2 + y2 = r2
What is the integral of a sphere?
An integrating sphere (also known as an Ulbricht sphere ) is an optical component consisting of a hollow spherical cavity with its interior covered with a diffuse white reflective coating, with small holes for entrance and exit ports. Its relevant property is a uniform scattering or diffusing effect.