IIT JEE , AIEEE Forum - Mathematics , Differential Calculus

shailesh_45

a box with a square base and open top is to be made from a material of area 192 sq m , find its dimensions so as to have max vol

srujana

Let the height be h

Given,the box has a square base, let its l=b be a

Surface area of the cube(open at one end) =a^2+4ah=192

Vol=f(a)=a^2.h

$=\frac{192-a^2}{4a}.a^2$

Equating the first derivative to 0,we get

$a=8\\<br/>\Rightarrow h=\frac{8}{3}$

shailesh_45

ans 8,8,4

srujana

sry...small calculation mstk

(192-64)/(32)=4=h

so the dimensions r 8,8,4

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