How do you find the area of a sphere in spherical coordinates?

i.e. x^2+y^2 = R^2 with z between -R and R. Any region on the sphere has the same area as the corresponding area on the cylinder. The correspondence is via a radial projection out from the z axis. So, for example, the area between latitudes would be 2pi*R^2(cos(phi1)-cos(phi2)).

How do you find spherical polar coordinates?

In spherical polar coordinates, h r = 1 , and , which has the same meaning as in cylindrical coordinates, has the value h φ = ρ ; if we express in the spherical coordinates we get h φ = r sin θ . Finally, we note that h θ = r . (6.21)

What is dA for a sphere?

where dA is an area element taken on the surface of a sphere of radius, r, centered at the origin. We have just shown that the solid angle associated with a sphere is 4π steradians (just as the circle is associated with 2π radians).

What is the curved surface area of a sphere?

4πr²
Since the sphere is a complete curved shape therefore the curved surface area is equal to the total area of sphere. It is also called lateral surface area. Surface Area of Sphere = 4πr², where r is the radius of sphere.

How do you find the area of a sphere?

The steps to calculate the surface area of a sphere is:

Step 1: Know the radius of the sphere.
Step 2: Take the square of the radius by multiplying it by itself.
Step 3: Multiply r2 by 4.
Step 4: Multiply the value of 4r2 by the approximate value of pi, that is, 3.14.
Step 5: At last, add the units to the final answer.

What is spherical polar coordinates system?

Are spherical coordinates Euclidean?

The spherical coordinate system is commonly used in physics. It assigns three numbers (known as coordinates) to every point in Euclidean space: radial distance r, polar angle θ (theta), and azimuthal angle φ (phi).

What is the volume element in spherical polar coordinates?

1), and the volume element is simply dV=dxdydz.

What is the area of the sphere?

Surface Area of Sphere = 4πr², where r is the radius of sphere. A sphere is a solid figure bounded by a curved surface such that every point on the surface is the same distance from the centre.

How do you find the distance between spherical coordinates?

In 3D Euclidean space, we know that distance between 2 points: a=(x1,y1,z1) and b=(x2,y2,z2) is s2=(x2−x1)2+(y2−y1)2+(z2−z1)2)from metric ds2=dx2+dy2+dz2.

What are the numbers in spherical polar coordinates?

Which is the element of volume in spherical coordinates?

In spherical polar coordinates, the element of volume for a body that is symmetrical about the polar axis is, (1) d V = 2 π s i n θ d r d θ. Whilst its element of surface area is, (2) d S = 2 π r s i n θ d r 2 + r 2 d θ 2.

How are the coordinates of a sphere determined?

In mathematics and physics, spherical polar coordinates (also known as spherical coordinates) form a coordinate system for the three-dimensional real space . Three numbers, two angles and a length specify any point in . The two angles specify the position on the surface of a sphere and the length gives the radius of the sphere.

What makes a spherical coordinate system a coordinate system?

In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a point is specified by three numbers: the radial distance of that point from a fixed origin, its polar angle measured from a fixed zenith direction, and the azimuth angle of its orthogonal projection on a reference plane that