Find the rate of change of total surface are of a right circular cone w.r.t. radius . (Cone angle remain constant ), when radius=5 cm.

Explanation

`A=pir^(2)+pi rl `, where l is slant height , `theta` is semivertical angle and r is radius .
`=pir^(2)+pir^(2) "cosec" theta , " "(l= r "cosec"theta)`
`=pir^(2)(1+ "cosec"theta)`
Differentiating with respected to r
`(dA)/(dr)=2pir (1+ "cosec"theta)`
`(dA)/(dr)|_(r=5cm)=10pi(1+"cosec"theta) cm^(2)//cm`