IIT JEE , AIEEE Forum - Mathematics , Differential Calculus

mona840

^/GUYS

this is an NCERT ques

The complete ques is

Show tat the semi verticle angle of a right circular cone of given surface area and maximum volume is sin^-1( 1/3)'

Heres de soln

S = r²+ r l .......(i)

l = (S -- r²) / r

V = 1/3 r²h

V²= 1/9 ²r⁴ ( l² -- r²)

put de value of l n solve it further u'll get

V²= 1/9 S (Sr²-- ²r⁴)

nw put Z = V²and differn wid respect to r

equate it to zero n get de value of S

tat comes out to b 4r²

Take double derivative wic comes out to b -- 4S²/ 9

itz less than zero so its proved to b de point of maxima

Z n V both r maxm at S = 4r²

so put tat in eqn (i) n solve

u'll get

l = 3r

nw

sin

= r/l = r/3r = 1/3

wher is de semi vertical angle

HENCE PROVED