Parts Of A Sphere Math

Like a circle in a two dimensional space a sphere is defined mathematically as the set of points that are all at the same distance r from a given.

Parts of a sphere math. The area of the smaller spherical cap of base radius r is given by s ρ 2πρ ρ ρ2 r2 where ρ is the radius of the sphere. The elements of a sphere are. The chord is the segment that joins any two points of the surface. The equation of a sphere is math x 2 y 2 z 2 r 2 math the spherical coordinates are.

Cosθ math equation of the sphere is. The part of the sphere x 2 y 2 z 2 b 2 that lies inside the cylinder x 2 y 2 a 2 where 0 a b. The radius is the distance of the center to a point of the sphere. It is also a spherical segment of one base i e bounded by a single plane.

This is a decreasing function of ρ when r is fixed so we have s t s r 4πr2. Math x ρ sinθ cosφ math math y ρ sinθ sinφ math math z ρ. The diameter is the chord that passes through the center. If the plane passes through the center of the sphere so that the height of the cap is equal to the radius of the sphere the spherical cap is called a hemisphere.

The center is the interior point equidistant to any point of the sphere. Sphere parts calculate the area of a spherical cap which is part of an area with base radius ρ 9 cm and a height v 3 1 cm. Sphere parts calculate the area of a spherical cap which is part of an area with base radius ρ 9 cm and a height v 3 1 cm.