The volume of a right circular cone of radius r and height h is V = 1 3 πr 2h (a) (i) Find a formula for the instantaneous rate of change of V with respect to r if r changes and h remain constant. (ii) Suppose that h = 2 is fixed but r varies. Find the rate of change of V w. R. To r at the point where r = 4.

(i) rh

(ii)

Explanation:

Given:

V = r²h

Where;

V = volume of a right circular cone.

r = radius of the cone

h = height of the cone.

(i) The rate of change of V with respect to r if r changes and h remains constant is , and is given by finding the differentiation of V with respect to r as follow:

= [r²h]

= rh     --------------------(i)

(ii)

Given;

h = 2

r = 4

Substitute these values into equation (i) as follows;

= (4 x 2)

= (8)

=

=

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