The ratio of numerical value of plane angle for a circle to solid angle for a sphere is:Required to answer. Single choice.
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Answer:
A plane angle is one that can be measured completely within a plane. This may be because the angle occurs in a 2-D space, or it is an angle that is contained completely within a plane that is in a 3-D (or higher-D) space.
So the angles in a triangle are plane angles, because they are in a plane. Similarly, the angles in a spherical triangle are plane angles, because even though they measure things in a 3-D space, they can always be shown to be wholly within a plane.
Another way to consider a plane angle is to think of angles within a circle. You can divide the circle up into 2π radians, for example, or 360°, or 400 gon, or whatever units you choose. However, the radian as a unit is defined by the subtended arc length that is equal to the radius of the circle.
A steradian, the basic unit, is solid angle is one that is subtended by a portion of the surface area of a sphere that is equal to r^2, where r is the radius of the sphere. It can be considered to be a cone subtended at the center of the sphere by a part of the surface of the sphere.
A sphere has a surface area of 4πr^2, so a sphere contains 4π steradians.
Perhaps the easiest way to picture a solid angle is the angle within the pointy end of a cone, as a solid, rather than as a plane.
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