Question

An open rectangular box with square base is to be made from 48 ft^2 of material. What dimensions will result in a box with the largest possible volume?

Answer 1

4,4,8
Let sides be x ,a,a
AS a^2+4ax=48
which gives x=(48-a^2)/4a
volume=a^2 x
Put value of x in this we get
V=(48a-a^3)/4
differentiating wrt a and equating to zerowe get
48-3a^2=0
a^2=16
a=4
hence x=8

Answer 2

Square base means length = width.
V = L*W*H = L^2 * H
SA = 2L^2 + 4LH = 2L(L+2H) = 48
H = 48/2L -L =(48-2L^2)/2L

V = L^2 * [(48-2L^2)/2L]
There's your fomula for volume in terms of 1 variable, Length. Take the derivative, solve for 0 to get critical points. CHeck those points.

Answer 3

If a=4, then x would be 2 wouldn't it. (48-(4)^2)/ (4(4) = 2

Answer 4

oh yes

Answer 5

calculation error!!!!

Answer 6

thanx for correcting that

Answer 7

V = 24L-L^3
That's the simplified form I get for volume.
V' = 24 -3L^2
24-3L^2 = 0
3(8-L^2) = 0
gives L = sqrt(8)

Answer 8

Dude its an open box

Answer 9

And if L = sqrt(8),
then H = (48-2L^2)/2L = 32/(2sqrt8) = 16/sqrt8

Answer 10

Hmph. So minor change in SA. Same method otherwise.

Answer 11

yess

Answer 12

What difference does it make it is an open box?

Answer 13

I guess it means SA = L^2 + 4LH
instead of 2L^2 + 4LH

Answer 14

open box doesnt count top one

Answer 15

@SmoothMath yess

Answer 16

Oh. Haha. Duh. Okay. Thank you guys.

Answer 17

it was pleasure helping u

Answer 18

SA = L^2 + 4LH = 48
H = (48-L^2)/(4L)
V = L^2H = L^2(38-L^2)/4L = (48L-L^3)/4
= 48L/4 -(L^3)/4
V' = 12 - 4L^2
Setting equal to 0 yields
4(3-L^2) =0
L = sqrt(3)

Answer 19

Oh hold on.
v' = 12 - (4/3)L^2

Answer 20

again incorrect

Answer 21

Lols. Okay.

Answer 22

v' = 12 - (3/4)L^2

Answer 23

Ah. Indeed.

Answer 24

:)