a right cone is inscribed in a sphere of radius R. Let S=f(x) be the functional relationship between the lateral surface area S of the cone and its gereratrix x then the find the value of f(R) and if x is such that x to the power n, n>= 6 is negligible then find S.

3 years ago

Share

Answers : (1)

                    

Hii vashuda


First of all before reading this...draw the geometry of the condition given....i am assuming that u have drawn a sphere a cone ...with


 


Slant height = x  radius of cone = r  and heigh of cone = h


Radiius of sphere = R after this read my solution


 


The height of the cone h = R + (something)


something = distance of centre from the base of the cone....you need to find this something okk


Let it be z


then by applying a few strength on mind you will get ..


z = root( R^2 - r^2)   [ because there is a small right angle triangle formed by side R , r and z with R as largest side )


 


Now surface area  S = π.r.x= f(x)


 


again x , h and r form a rt.angled triangle..


 


x^2 = h^2 + r^2  => x^2 = (R+z)^2 + r^2    =  R^2 + z^2 + 2.z.R + r^2


 


x^2 = R^2 + R^2 -r^2 +  2.root(R^2-r^2).R + r^2 


x^2 = 2.R^2  + 2.root(R^2-r^2).R 


now put x=R


R^2 = 2.R^2 + 2.root(R^2 -r^2).R


 


-R^2 = 2.root(R^2 -r^2).R


-R = 2.root( R^2 -r^2)


 


R^2 = 4.(R^2 - r^2)


4r^2  = 3R^2


 


or  r = R.root(3)/2 --------(1)


 


f(x) = pi.x.r


 


So f(R) = pi.R.( R.root(3)/2 ) =  root(3).pi.R^2 / 2    ans ....


 


If u r unable to understand my steps...then please ask furthure...


 


Regard


Yagya


aksiitians_expert

3 years ago

Post Your Answer

More Questions On IIT JEE Entrance Exam

Ask Experts

Have any Question? Ask Experts
Post Question
Answer ‘n’ Earn
Attractive Gift
Vouchers
To Win!!!
Click Here for details