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Question

The volume of a cylinder of height 9 inches and radius rinches is given by the formula V=9πr2.

Which is the correct expression for dVdt?

1. dVdt=0
2. dVdt=18πrdrdtdhdt
3. dVdt=18πrdt
4. dVdt=9πr2drdt
5. dVdt=18πrdrdt

Suppose that the radius is expanding at a rate of 0.2 inches per second. How fast is the volume changing when the radius is 2.8 inches?  Use at least 5 decimal places in your answer.

Answer 1

last option is correct

more economically written as:

V'= 18pirr' where V'=dV/dt and r'=dr/dt

for r' = .2

and r = 2.8

V'= 18pi(2.8)(.2) = 252pi/25= 1008pi/100

= 10.08pi

= 27.40028083 in^3 per second

V= hpir^2

h= 9 inches, r=2.8 inches

V= 9pi(2.8)^2 = 191.8019658 cubic inches

in one second

V = 9pi(3^2) = 9pi(9) =81pi = 220.1808281 in^3

in one second V increases about 27.40028

191.80197 + 27.40028 = 219.0225 which is close to 220.1808281

closer than 1 difference