Question

the radius of a cylinder is increasing at a rate of 1 metre per hour, and the height of the cylinder is decreasing at a rate of 4 metres per hour, at a certain instant , the radius is 5 metres and the hight is 8 metres. what is the rate of change of the volume of the cylinder at the instant?​

Answer 1

Answer:

Given

dt

dr

=1 and

dt

dh

=−1

We know that, Volume of a cylinder is given by

V=πr

2

h

⟹

dt

dV

=π2rh

dt

dr

+πr

2

dt

dh

⟹

dt

dV

=πr(2h(1)+r(−1))

=π×5(2×15−5)

=125π