Question

Determine the dimensions of a rectangular solid (with a square base) with maximum volume if its surface area is 100 meters.

Answer 1

Let x be the side of the square base and h be the height.
Volume V = ?
Surface Area = ?

Answer 2

well the surface area is 100

Answer 3

Yeah, but what is the surface area in terms of x and h?
what is the volume in terms of x and h?

Answer 4

A rectangular solid with a square base has 2 squares (top square & bottom square).
It has 4 rectangles (4 sides)
Add up the areas of 2 squares of side x and 4 rectangles of sides x and h.

Answer 5

v=x(h)

can't think of sa off the top of my head right so im going to guess its sa=0.5(x)(h)?

Answer 6

A rectangular solid is a prism.
Volume of a prism = area of base * height

Answer 7

Volume V = x^2 * h ----- (1)
Surface area = 2 * x^2 + 4 * x * h = 100 ------ (2)

From (2), find h. Substitute h in (1). Now you will have V as a function of just one variable, namely, x.
To maximize V, find dV/dx, equate it to zero and solve for x.

Answer 8

ok ill work on it. thank you!

Answer 9

You are welcome.

Answer 10

ok @ranga i got base side=(10√6)/3 and height=(5√6)/3

Answer 11

I am getting x = (5√6)/3.
But I will have to cjhck my calculations again.

Answer 12

i was getting all kinds of things for x and (5√6)/3. just rechecked it again and thats what i got. did we get the same thing for h though?

Answer 13

I am getting x = (5√6)/3 and h = (5√6)/3.
So the solid turns out to be a cube which seems right to me.

Answer 14

ok