Sphere

Sphere

Sphere

We see many solids like cricket ball, tennis ball, basket ball, football, globe etc. All these are the examples of spheres. Let us know some more facts about the sphere.

Examples of sphere

A sphere cab be described as the set of all those points in the space which are at equal distance from a fixed point. The fixed point is called centre and the constant distance is called the radius of the sphere.

3D Sphere

In the given figure above, O is the centre of the sphere and distances OA, OB, OC, OD, OE, OF are the radius of the sphere.

A line segment passing through the centre of the sphere with its end points on the sphere is called the diameter of the sphere. In the given figure above  AB, CD and EF are the diameters of the sphere.

Surface Area of a Sphere

Take a cylinder of equal height and diameter and a sphere equal diameter with the cylinder and wrap the sphere with a rope and with the same rope the curved surface area of the cylinder can be wrapped.

Surface Area of a Sphere

Surface area of the sphere = Curved sufrace area of the cylinder
                                               = 2πrh
                                               = 2πr × 2r    [ h = d = 2r]
                                               = 4πr2
Thus, if r is the radius of a sphere then the surface area of the sphere is 4πr2.

Volume of Sphere

Take a cylinder of equal height and diameter and a sphere of equal diameter with the cylinder. Fill the cylinder with water and drop the sphere into the cylinder, then two-third of water flows out. 

Volume of Sphere

So we can say that,
Volume of sphere = 2/3 volume of the cylinder
                             = 2/3 × πr2h
                             = 2/3 × πr2 × 2r    [ h = d = 2r]
                             = 4πr3/3

Thus, the volume of the sphere of radius r is 4πr3/3.

Workout Examples

Example 1: Find the total surface area and the volume of the given cricket ball of radius 35mm.
cricket ball

Solution: Here,
                          Radius of cricket ball (r) = 35mm
                Now,
                          Total surface area (TSA) = 4πr2
                                                                    = 4 × 22/7 × (35mm)2
                                                                    = 4 × 22/7 × 1225mm2
                                                                    = 15400 mm2

                          Volume (V) = 4πr3/3
                                              = 4/3 × 22/7 × (35mm)3
                                              = 88/21 × 42875mm3
                                              = 179666.67mm3

                Thus, the total surface area of cricket ball is 15400 mm2 and the volume is 179666.67mm3.


Example 2: If the total surface area of a solid sphere is 616cm2, what will be its radius?

Solution: Here,
                           Total surface area of sphere (TSA) = 616cm2
                i.e.      4πr2 = 616
                or,      4 × 22/7 × r2 = 616
                or,      88/7 × r2 = 616
                or,      r2 = 616 × 7/88
                or,      r2 = 49
                or,      r2 = 72
                or,      r = 7cm

                Thus, the radius of the solid sphere is 7cm.


Example 3: Find the total surface area of a sphere whose volume is 1372π/3 cm3.

Solution: Here,
                           Volume of sphere = 1372π/3 cm3
                i.e.      4πr3/3 = 1372π/3
                or,      4r3 = 1372
                or,      r3 = 1372/4
                or,      r3 = 343
                or,      r3 = 73
                or,      r = 7cm

                Now,
                           Total surface area (TSA) of sphere = 4πr2
                                                                                       = 4 × 22/7 × (7cm)2
                                                                                       = 4 × 22/7 × 49cm2
                                                                                       = 616cm2

                Thus, the total surface area of the sphere is 616cm2.


You can comment your questions or problems regarding the area and volume of sphere here.

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