Answer:
The height that make the surface area as small as possible is 10 cm
Step-by-step explanation:
Let
L -----> the length of the base of the box
W -----> the width of the base of the box
H ----> the height of the box
we know that
The volume of the box is equal to
we have
so
----> equation A
------> equation B
substitute equation B in equation A
Solve for H
-----> equation C
The surface area of a open box is equal to
----> equation D
Substitute equation B and equation C in equation D
Convert to function notation
Find the derivative
set equal to zero
Solve for W
<em>Find the value of L (equation B)</em>
<em>Find the value of H (equation C)</em>
therefore
The height that make the surface area as small as possible is 10 cm