Question

Determine the dimensions of a rectangular solid (with a square base) of maximum volume if its surface area is 150 square inches. (Using Calculus)

Answer 1

if it helps i know the answer is 5x5x5 i just dont know how to get that

Answer 2

You don't have to use calculus... will you get it wrong if you don't?

Answer 3

I mean why cant you just use the formula for surface area and set that equal to 150 and solve for x.

Answer 4

yes. :P i know how to do it w/o calc but we are in the section about finding max and min using derivatives.

Answer 5

okay, i figured it out... are you still around?

Answer 6

ya hah

Answer 7

lol, okay all we need to do is use our given info for surface area and write an equation for that in terms of x and y, x for the base and y for the height, y must be different because we are not sure if it is the same as x or not, they didnt tell us... all they told us was that the base was square... so can you write that equation?

Answer 8

dont you have to have width too? because its a solid

Answer 9

well sure, length x width x height... but it said the base was a square, so we know the length and the width are both the same.... x.... but the height we dont know... and that would be y...

so if i said just find the area of the base, just the base, in terms of x, what would that be?

Answer 10

oh wow that makes way more sense haha. so a=xy

Answer 11

well the base is square... so it is just x times x, so x^2, and we have two of them, the bottom and the top of the shape right?

Answer 12

now we just have to add that to the area of the 4 sides around the shape...

do you know what the expression would be for the area of the sides?

Answer 13

so the surface area would equal 2x^2 +4(xy)
sorry im really bad at this :/

Answer 14

Refer to the Mathematica solution attached.

Answer 15

yes fantastic... and all that will equal 150

so we have 2x^2+4xy=150

now we have to solve for y

Answer 16

ok give me a minute or two

Answer 17

ok

Answer 18

(75-x^2)/(2x) ?

Answer 19

looking good... I would write that as the difference of the two factions though...