Question

For a closed rectangular box, with a square base x by x cm and height h cm, find the dimensions giving the maximum volume, given that the surface area is 10 cm^2.

write EXACT answers...

x=______
h=______

thank you!! where do i start?? :O @Luigi0210 :)

Answer 1

@ganeshie8 can help.. I don't understand optimization either

Answer 2

ahh okay thanks!!

Answer 3

not sure if @ganeshie8 is there hahaa

Answer 4

Write out the SA equation, just add up the area of all the sides, and set it equal to 10.

Use that equation to solve for h in terms of x.

Volume is area of base times height.

Differentiate the volume, set equal to zero, solve for x. Then use x to find h.

Answer 5

would that be l*w*h ?

Answer 6

Yes, but use x and h.

Answer 7

okay

like this?

x* h * l ?

not too sure what that means haha

Answer 8

how would the SA equation look?

Answer 9

I would draw a diagram, it will make it easier for you to visualize it and find the SA. The dimensions are x by x by h, so there's no need for L.

Answer 10

okay

so it will be x * h = surface area?

Answer 11

(x*h)^4 ?

Answer 12

The base and top has area x*x

There's 4 sides with area x*h

Add them all up

Answer 13

(x*h)+(x*h)+(x*h)+(x*h) ?

Answer 14

You're missing the base and top.

Answer 15

so (x*h)+(x*h)+(x*h)+(x*h)+(x*h)+(x*h) ?

Answer 16

The base and top have area x*x

There's 4 sides with area x*h

Add them all up

Answer 17

https://www.google.com/search?q=finding+surface+area+of+a+rectangular+prism&oq=finding+suface+area+of+a+&aqs=chrome.1.69i57j0l5.6431j0j4&sourceid=chrome&es_sm=93&ie=UTF-8

Answer 18

Your SA = 4xh + x^2 = 10

solve it for h then follow the steps in the first post.

Answer 19

\[\Large V = x^2 h\]

Answer 20

so

4xh = 10-x^2

h= 10-x^2
-------
4x

? @agent0smith

Answer 21

and then\[V=(x ^{2})(\frac{ 10-x^{2} }{ 4x })\] ?

Answer 22

and then derivative is this? \[V'=\frac{ 5 }{ 2 }-\frac{ 3x^{2} }{ 4 }\] ?

Answer 23

then set equal to zero?