For a hemisphere solid angle is measured asa)Radian and its maximum value is πb)Degree and its maximum value is 180 degreec)Steradian and its maximum value is 2πd)Steradian and its maximum value is πCorrect answer is option 'D'. Can you explain this answer?

Question

For a hemisphere solid angle is measured asa)Radian and its maximum value is &pi;b)Degree and its maximum value is 180 degreec)Steradian and its maximum value is 2&pi;d)Steradian and its maximum value is &pi;Correct answer is option 'D'. Can you explain this answer?

Answer

4π steradians.

The solid angle is a measure of the amount of space an object or region occupies in three-dimensional space, as seen from a specific point. It is measured in steradians (sr), which is a unit of solid angle in the International System of Units (SI).

For a hemisphere, the maximum possible solid angle is equal to the total surface area of the hemisphere divided by the square of its radius. The total surface area of a hemisphere is 2πr^2, where r is the radius.

Therefore, the maximum possible solid angle for a hemisphere is given by:

Maximum solid angle = (2πr^2) / r^2 = 2π

This means that the maximum solid angle for a hemisphere is 2π steradians, which is equivalent to 4π in radians.

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