Sunday, October 30, 2016

Mensuration ,mathematics on right angled cone and on spheres

Students are  asking for the mathematics which they are not understanding in the email;    kaacconsultant@gmail.com . Solution is appearing in this page for helping others also. 





The problem is  The slant height of a right circular cone  is 10 m and its height is 8 m. find the area of the curved surface.


right circular cone means ,its base is a circle the meaning of the right is , its peak is straight  at 90 degrees. above the center of the base .

slant height means ,distance of the peak from the any point of base perimeter


height is   8 meter

slant height is 10 meter

from the above data we have to deduce another date , which is the radius of the base, otherwise we will not be able to find curved surface area.

radius of the base is 6 meter.  ( I have not deduced the same , students have to apply their skill) if not otherwise contact.

Now area of the curved surface is   pi * radius* slant height value of    pi has taken as = 3.142

which  will  become  187.52 sq meter     why  square meter ? because to units of meters has been multiplied.


Suppose there are two spheres  having radius R and r , is there any relation can be established   with this two radius. let us try

Surface area of the sphere with  radius  R  = 4 * pi* R2 ( R square)
similarly surface area of the sphere with radius r = 4*pi* r2 ( r square)

ratio is coming as R2 / r2 or  (R/r)2

Problem
A cylindrical shaped article has a height of 20 Cm.The radius of its base is 21 cm. and its volume is 
2310  cm 3
It is open at the top
Find the cost of painting it from otside when rate is  Rs. 5 per Cm 2
Solution
Given data : 
Height  H 20 Cm
Radius of the base R 21 Cm
Volume V 2310  cm 3
Now as the cylinder is open at the top , surface area we have to find out at the cylinder wall and the bottom
surface area of the cylinder   2 π R L
2640 cm 2
surface area of the bottom π R 2
1386 cm 2
Total area to be painted surface  + bottom
4026 cm 2
And cost of painting is Rs. 5 per square Cm
That is one square Cm will cost  Rs. 5
But we have  4026  cm 2 Rs. 5*4026 cm 2
Rs. 20,130  will be cost. 

No comments: