Our Discord hit 10K members! 🎉 Meet students and ask top educators your questions.Join Here!

# The surface area of a right-circular cone of radius $r$ and height $h$ is $S=\pi r \sqrt{r^{2}+h^{2}}$ , and its volume is $V=\frac{1}{3} \pi r^{2} h_{\text { . }}$$$\begin{array}{l}{\text { (a) Determine the ratio } h / r \text { for the cone with given surface area } S \text { and }} \\ {\text { maximum volume } V .} \\ {\text { (b) What is the ratio } h / r \text { for a cone with given volume } V \text { and mimimum }} \\ {\text { surface area } S ?} \\ {\text { (c) Does a cone with given volume } V \text { and maximum surface area exist? }}\end{array}$$

## a) $\sqrt{2}$b) $\sqrt{2}$c) Therefore, the maximum surfaces area does not exist to the cone with given volume $V$ .

#### Topics

Functions

Partial Derivatives

### Discussion

You must be signed in to discuss.
##### Catherine R.

Missouri State University

##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

Lectures

Join Bootcamp

### Video Transcript

and our problem have crescent Recall with radius are high H and Seidlin's off, and we have to equation the 1st 1 force if Syria and 2nd 1 is sports by using the equations by using the vision off area first, we want to define that l square equal rules edge squared loss or squares. Next weekend. Use the equation off surface area, which would be what a we take the square of it. Equal boy squared or squeals off. The blowing is square, thus or school from this, we can get the function force height, which is because pitch square you cool. Hey, squares minus boy or four over, Boy squared off squares. We have another question for civilian Jessica for you before 1/3 boy or square leech Weakens Institute is a hive. Inside the secretive, they will get a one over Stry boy or squared of deploy rule. He squealed. When's boy or for four? Over? Oh boy. Oh, This or will be removed with this square and this boy being with this boy, we will have V before 1/3 or a square mine's boy square or or four or bar. Oh, we want William to be maximum silicon. Say that David Volume Boy D or you could see you. This will be equal to 1/3. My or these were mine's boy squirrel Oh boy. Or or four OLB or negative off blowing Negative for sward or cubes Lows. A schoolroom this world way Be right. Pose region again soon for three. Oh, going or loi is square minus boy squared O R. Or full or born in it Oh, deploy narrative Four boys works three or plus he's full range Boy square or or four or more Oh, by taking a going to the miniter and simplification, we will have negative three or 44 Boy squirm Los a squirrel four Siri. But the blue good Lord is for minus boy screws off bore four. Because to receive, we can say that. Just eliminate this one. Numerator is equal to zero. So we would have negative three more fool longer squared Los Hey square. It was 20 from this will have on the square and B squared because to three board for boy screwed. We were already having an equation for the A square by on by quick equating this according sister equations we will get and boy squared Oh, squirrel on the blowing and she square plus or square equals 23 or 44 longer school And for this we would have this are square and would be it used to And this boy square would be removed with this by square on, we finally have an edge over our issue. If we're good, you'll This is a report. This is our first report For our second requirement. We will apply the same come concept, but or different occasions. You already have an H because to three Wien boy or squares from the vision of William and have on we also have an s square which is safe cereal. It won't boy square R squared off deploy H square plus own squirt. But taking by removing this each and substituting with this one we will have and is equal is squirt Will be was too boring square are square blowing de re squared Boy square are both four plus or squirt. We want the service area Toby maximum to be minimum story So the D is boy de or with sequence to zeal will be equals toe to us off the Loi de s Boy D or it won't Negative 18. These quote 00 are pure plus four boys, squirrels or cubes. Therefore, we would have Yeah, do boy squared a war six. It was to lying the square because to nine off the place aggression of volume which is 1/9 boy squared or or four age squares. This will be the one to just one. Is this by square? Beautiful Visits by square are both for be recused on and this would be reduced r squared. We will finally have get to r squared because to age square this will give us an age or are also equal to to for all sent and final department We can let we can take a constant value off the volume left V equals to one. For example Therefore, one of those three boy are square age is beato because toe won their fourth will be pulled three over boy or squares This can employs it at our turns to infinity Well done 20 which means we're taking limit Example limit oh turns to infinity each turns zero is off or on each will be equals to finish this news that Yes, this means that s does no, uh, maximum value. Um, is there course dream? And is it for no horn? Oh, good. Very. And Mexico Service areas. You just thank you.

#### Topics

Functions

Partial Derivatives

##### Catherine R.

Missouri State University

##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

Lectures

Join Bootcamp