Question

HELPPP!!

Find the dimensions of a box with a square base with
(a) volume 12 and the minimal surface area
(b) surface area 20 and minimal volume

Answer 1

The rate of change of volume is surface area ... in other words, as fast as the surface area changes, so does the volume

Answer 2

Sa = 4(b*h) + 2(b*b)

assuming its a solid box with 4 sides and a top and bottom

Answer 3

V = b*b*h

12 = b^2 h

h = 12/b^2

Answer 4

Sa = 4(b*h) + 2(b*b)

Sa = 4(b*12/b^2) + 2b^2

Sa = 48/b + 2b^2

we can find min or max with the first derivative

Sa' = -48/b^2 + 4b

Sa' = -48 + 4b^3/b^2 = 0 when:

-48 + 4b^3 = 0

-12 + b^3 = 0

b = cbrt(12) , maybe