Note on Sphere

A Sphere can be described as the set of all points in space which are equidistant from a fixed point. The fixed point is called the centre of the sphere and the constant distance is called its radius. A line segment passing through the centre of the sphere with its end points on the sphere is called a diameter of the sphere. All diameters of a sphere are of the same length, being equal to twice the radius of the sphere. A sphere can also be considered as a solid generated by revolving a circle about a diameter.

A plane passing through the centre of a sphere divides the sphere into two equal parts. Each part is called a hemisphere.

For a sphere of radius r, we have

(i) Surface area = 4Πr²

(ii) Volume = 4/3Πr²

For a hemisphere of radius r, we have

(i) Curved surface area = 2Πr²

(ii) Volume = 2/3Πr²

(iii) Total surface area = 2Πr² + Πr² = 3Πr²