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.

Question

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

Answer 1

That's only 40 cubic feet.

Answer 2

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.

Answer 3

How about 5 by 4 by 4?

Answer 4

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

Answer 5

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?

Answer 6

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.

Answer 7

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

Answer 8

So, how do you solve it? Steps please!

Answer 9

Anyone answer me?

Answer 10

i got 5 by 4 by 4

Answer 11

No you need to find the surface area

Answer 12

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

Answer 13

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

Answer 14

I don’t understand how to solve it

Answer 15

Obviously no

Answer 16

the answer is in feet and what is it
some people say it is 5ft*4ft*4ft=80 cubic feet

Answer 17

4 ft, 4 ft, and 5 ft

Answer 18

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

Answer 19

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

Answer 20

ye bros