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High School Mathematics
4.21 Important Points in Sphere

1. The solid obtained by rotating a semi circular plane with its diameter as axis is a sphere.

2. Any point on the surface of the sphere is equidistant from a fixed point in the interior of the sphere. This fixed point is called the centre of the sphere.

3. The line segment joining the centre of the sphere to any point on its surface is called the radius of the sphere.

4. As the sphere has only one surface namely curved surface its curved surface area and total surface area are not different.
Curved surface area = 4 * pi * r2

5. Volume of sphere = 4/3 * pi * r3

6. The volume of a sphere of radius r is equal to the volume of the cylinder whose base radius is also r and height (4/3)r.

7. A plane through the centre of the sphere divides the sphere into two equal parts and each is called a hemisphere.
curved surface area of the hemisphere = Curved surface area + Area of the plane circular surface
= 2 * pi * r2 + pi * r2
= 3 * pi * r2

8. A spherical shell can be regarded as the difference between two concentric spheres.

9. A spherical shell has a finite thickness which is the difference of the radii of the two solid spheres which determine it.


Name: ___________________

Date:___________________

High School Mathematics
4.21 Important Points in Sphere