- #1

- 2,374

- 305

- Homework Statement
- The volume of a cylinder is given by the formula ##V=πr^2h##. Find the greatest and least values of ##V## if ##r+h=6##

- Relevant Equations
- rate of change- differentiation

$$V=πr^2h$$

$$V=πr^2(6-r)$$

$$\frac {dV}{dr}=12πr-3πr^2$$

For max/min value, $$\frac {dV}{dr}=0$$

$$12πr-3πr^2=0$$

$$3πr(4-r)=0$$

##r=0## or ##r=4##

$$⇒V_{max}= 32π$$

$$⇒V_{min}= 0$$,

I do not think there is another way of doing this...

$$V=πr^2(6-r)$$

$$\frac {dV}{dr}=12πr-3πr^2$$

For max/min value, $$\frac {dV}{dr}=0$$

$$12πr-3πr^2=0$$

$$3πr(4-r)=0$$

##r=0## or ##r=4##

$$⇒V_{max}= 32π$$

$$⇒V_{min}= 0$$,

I do not think there is another way of doing this...

Last edited: