Question

the semi vertical angle of a cone is 45 degrees. then the rate of change of its volume is : a) curved surface area times the rate of change of r b) base area times the rate of change of l c) base area times the rate of change of r d)none of these

Answer 1

Question:

the semi vertical angle of a cone is 45 degrees. then the rate of change of its volume is :

Method of Solution:


In this Question, It is given that the semi vertical angle of a cone is 45 degrees. then the rate of change of its volume .

Now,

Let the Height of cone be h cm

Let the radius of cone be r

Now, According to the Question's Statement!


We know : [tan 45° = 1]

Tan 45° = r/h

1 = r/h

[h=r] -----(1)

Volume = 1÷3πrh


From Equation (1)

Volume = 1/3πr³

Differentiate between times.

DV/dt= πr² × Dr/DT

DV/DT = It is Equal to base area

Then, Dv/Dr = (Dr/dt) => Base area


From Option...


Option C is the Correct Answer.


[base area times the rate of change of radius]

Answer 2

Heya mate
The answer of ur question is in pic



So , the correct answer is C
i.e. Base area times the rate of change of r



hope it helps