A container needs to package hazardous chemicals in a special plastic rectangular prism that holds 80 cubic feet. Find the whole number dimensions of the container that would use the least amount of plastic.

My answer is 5ft, 2ft, and 4ft

How about 5 by 4 by 4?

I learned that surface area is pb(h)+2ba

so 5x4x4 would be
18(4)+2(20)
72+40
112
and the 10x4x2 would be
28(2)+2(40)
56+80
136
therefore a 5x4x4 box would have the least surface area

In order to use the least amount of plastic, you need to find the surface dimensions of this box.

If your box is 10 by 4 by 2 --

2(10*4) + 2(4 * 2) + 2(2*2) = ?

What are the surface dimensions of a box 5 by 4 vy 4?

4 ft, 4 ft, and 5 ft

That's only 40 cubic feet.

Let the dimensions of the box by x by y by z

xyz = 80
z = 80/(xy)

"least amount of plasic" implies least surface area
SA = 2xy + 2xz + 2yz
= 2xy + 2x(80/(xy)) + 2y(80/(xy))
= 2xy + 160/y + 160/x

now we know that xyz = 80
and 80 = (2)(2)(2)(2)(5)
combinations of x y z and SA
2 2 20 168
2 4 10 136
2 8 5 132
4 2 10 -- same as 2 4
4 4 5 112

So there are 5 different combinations we can use to get the volume of 80, but
to have the least surface area would be
4 by 4 by 5, as Ms Sue had suggested.

No you need to find the surface area

Reiny might be right. It does sound resonable to do that

Obviously no

But the question asks for the least amount of plastic to be used. Therefore, wouldn’t 2ft x 5ft x 5ft be better?

And wouldn’t 3ft x 4ft x 4 ft be even better?

ye bros

I did the problem again and my answer is 10x4x2= 80 cubic feet. Is my answer correct and could I have chosen different numbers.

Thanks.

Please can you tell me why you chose these numbers 5by4by4? Was my answer wrong. I am trying to get a better understanding of this problem in the event I have one similar to it on a test.

thank you so much

i got 5 by 4 by 4

the answer is in feet and what is it

some people say it is 5ft*4ft*4ft=80 cubic feet

So, how do you solve it? Steps please!

Anyone answer me?

I agree with smart pants. I was forced into pre at math and I'm super lost

I don’t understand how to solve it