WORKBOOK -EQUAL FRACTIONS -B.Ed Calicut university second semester task

SURFACE AREA OF A SPHERE

 A sphere is a solid figure bounded by a curved surface such that every point on the surface is the same distance from the centre.   In other words, a sphere is a perfectly round geometrical object in three-dimensional space, just like a surface of a round ball. The surface area of a sphere is defined as the amount of region covered by the surface of a sphere and is equal to 4πr².

 

What is the Sphere?

A sphere is mathematically defined as the set of points that are all at the same distance from a given point but in three-dimensional space.

The distance from the centre to the edge is called the radius of the ball, and the line that connects two points on the sphere and is twice the length of the radius is called as diameter.

 

 

Surface Area of Sphere

A sphere is the 3- D shape where the curved surface area equals to the total surface area of the figure. The curved surface area is the area in which only the area of the curved part is covered. The formula does not take into account the circular base.

The total surface area, on the other hand, is a combination of the curved area along with the area of the base The formula for the total surface area  and the curved surface area of the sphere is given below

Surface area (TSA) = CSA = 4πr² square units

How do you Find the Total  Surface Area of a Sphere?

To find the area of the sphere firstly, find the radius of the sphere. Secondly, apply the formula and simplify.

 This is what we do actually to find the surface area of a sphere just going through formulas here from our practical life we can identify how the surface area of the sphere become 4πr².

 ACTIVITY TO MAKE PRACTICAL IDEA OF SURFACE AREA OF SPHERE

Give pupils an orange and a blank sheet of paper. They have to draw circles around the orange onto the paper. The idea is that the circles on the paper should have the same radius as the orange. They draw as many circles on the paper as possible.

Then get the pupils to peel the orange and arrange the peel so that it fills the circles they drew on the paper. Some careful ‘sculpting’ of the peel will be required to get it to fill the circles with no gaps or overlaps. Pupils should fully fill one circle with peel before moving onto the next circle and so on.

A beautiful image should arise whereby the peel completely fills four of the circles proving the surface area of the sphere is  4πr².

 

Is there is any use of MATHEMATICIAN TO SOCIETY?

While studying PG this thought came to my mind several times.What is the purpose of studying this long theorems?,Even our teachers were not able to tell what is the use of studying this theorems they tell this is what is called  pure Mathematics not the applied one .Here am trying to find the beauty of mathematics and how it's contributing to society .

                     Mathematics has its own intrinsic beauty and aesthetic appeal, but its cultural role is determined mainly by its perceived educational qualities. The achievements and structures of mathematics are recognized as being among the greatest intellectual attainments of the human species and, therefore, are seen as being worthy of study in their own right, while the heavy reliance of mathematics on logical reasoning is seen to have educational merit in a world where rational thought and behavior are highly valued. Furthermore the potential for sharpening the wit and problem-solving abilities fostered by study of mathematics is also seen as contributing significantly to the general objectives of acquiring wisdom and intellectual capabilities
                                   
                                          
                The "functional" aspect of mathematics stems from its importance as the language of science, engineering and technology, and its role in their development. This involvement is as old as mathematics itself and it can be argued that, without mathematics, there can be neither science nor engineering. In modern times, adoption of mathematical methods in the social, medical and physical sciences has expanded rapidly, confirming mathematics as an indispensable part of all school curricula and creating great demand for university-level mathematical training. Much of the demand stems directly from the need for mathematical and statistical modelling of phenomena. Such modelling is basic to all engineering, plays a vital role in all physical sciences and contributes significantly to the biological sciences, medicine, psychology, economics and commerce.