I am suppose to be finding the max volume ofr a rectangular solid with a square base. I am having trouble coming up with the volume formula for such a figure. can someone help?

Question

anonymous · Answer

you must have some constraint yes?  like the area of the sides or the dimensions of a piece of paper?

amistre64 · Answer

area of base times height of solid

anonymous · Answer

got it

anonymous · Answer

if the area is fixed make a cube

amistre64 · Answer

$$\int_{0}^{h} x^2dx$$

anonymous · Answer

is it   
              1
            ---pi * a^2*h        ?
              3

anonymous · Answer

unless you don't need the top.  then it changes. not sure what the exact problem is, but you stated you need a maximum so i am thinking that this is a calc problem with something fixed

amistre64 · Answer

i think my fancy shmancy way is off :)

anonymous · Answer

yeah it is off.  and there is no pi in this either.

anonymous · Answer

yea no pi ....  :)

anonymous · Answer

pi  makes everything better.

amistre64 · Answer

dont need a pi to get area of a square ... just gotta sum up the areas up to the height

anonymous · Answer

usually area is fixed. so if area = A and you don't need a top then base is 
$$x^2$$ height is 
$$h$$ and volume is 
$$V=x^2h$$ which given that 
$$A = x^2+4xh$$ allows you to solve for h  as 
$$h=\frac{A-x^2}{4x}$$and gives 
$$V(x)=x^2\times \frac{A-x^2}{4x}$$ so something like that.

anonymous · Answer

then find the max by taking derivative etc etc

anonymous · Answer

sir joemath please answer my question

anonymous · Answer

what does x represtn in this ewuation?