

The Lagrangian is

with partial derivatives (all set equal to 0)

for
, and

Substituting each
into the second sum gives

Then we get two critical points,

or

At these points we get a value of
, i.e. a maximum value of
and a minimum value of
.
40 * 7.85 = 314
32.24 + 24.02 + 24.53 = 80.79
314 - 80.79 = 233.21
Answer is D
If you want an aquarium in shape of a cube with volume of 8000, then use the formula for volume of cube to find the length of one side:
V = s^3
where
s = side length
Substitute,
8000 = s^3
s = cuberoot(8000)
s = 20 inches
Well, if you have to draw this on a graphing paper, you should first make a scale to fit the drawing, like 1 inch = 0.5 cm, so a side length of 20 inches is equivalent to 10 cm on your graphing paper.
Hope this helped!