1. ## rate change

The volume of a closed cylinder of constant height 8cm is given by V=8(pi)r(squared). The radius of its base is 6cm and is increasing at the rate of 0.04cm/s

a) at what rate is the volume of the cylinder increasing? (to 2 decimal places)

b) at what rate is the total surface area of the cylinder increasing (to 2 decimal places)

I just need to verify my answers with someone quickly. thanx.

2. Originally Posted by chrisgo
The volume of a closed cylinder of constant height 8cm is given by V=8(pi)r(squared). The radius of its base is 6cm and is increasing at the rate of 0.04cm/s

a) at what rate is the volume of the cylinder increasing? (to 2 decimal places)
just solve for $\displaystyle \frac{dV}{dt}$ and plug in r and $\displaystyle \frac{dr}{dt}$

$\displaystyle 16\pi (6) (0.04)$

Originally Posted by chrisgo
b) at what rate is the total surface area of the cylinder increasing (to 2 decimal places)

I just need to verify my answers with someone quickly. thanx.
also just solve for $\displaystyle \frac{dT}{dt}$ and plug in $\displaystyle \frac{dr}{dt}$
where $\displaystyle T = 2\pi r^2 + 2\pi r h$