Question

a solid rectangular brick is to be made from 1 cu feet of clay. the brick must be 3 times as long as wide the width of brick for which it will have minimum surface area is a find a^3

Answer 1

if the dimensions of rectangular brick are x,a,y then x*a*y=1 and
x=3a and what else can be done are will be 2(xy+ya+ax) and to minimise it i need to differentiate it and put it zero i did it but the answer wont match so pl could anyone help me

Answer 2

wat did u get for a^3 ?

Answer 3

i got something like this
2(18a^3+3a^2-1)=0 i cant simplify it further the options given are
(2/9),(2/9)^(1/3),8/729,3/2

Answer 4

im getting 2/9

Answer 5

surface area : 2(xy+ya+ax)
substitute x and y values in terms of a

Answer 6

x = 3a *****
xay = 1
3a^2y = 1
y = 1/(3a^2) ****

Answer 7

surface area : 2(1/a + 1/(3a) + 3a^2)

minimize this

Answer 8

ok thanks i was doing it wrong i got the surface area wrong

Answer 9

happens... np :)

Answer 10

hey but how did u solved the cubic that we got on differentiating

Answer 11

u wil get an easy expression, pen down and see...

Answer 12

s=2(1/a+1/(3a)+3a^2)
s'=0=2(-1/a^2 -1/(3a^2) +6a)
-1-1/3+6a^3=0
so 4/3=6a^3
so a^3=2/9 itsnt it?

Answer 13

looks good !

Answer 14

thanks a lot

Answer 15

u wlc :)