The volume of a right circular cone of radius x and height y is given by V =(1/3)πx^2y . Suppose that the volume of the cone is 96π cm^3 . Find dy/dx when x = 6 and y = 8 .

Answer 1

This problem is a bit uncharacteristic for related rates - but here goes!

If V = (pi/3)*x^2y given V = 96pi then

x^2y = 288 now differentiate implicitly keeping in mind both the product and chain rule!!

d/dx (x^2y = 288) = 2xy + x^2(dy/dx) = 0

Now plug in x and y

2(6)(8) + 36(dy/dx) = 0

36(dy/dx) = - 96

dy/dx = -96/36