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 October 7th, 2012, 06:17 AM #1 Member   Joined: Sep 2012 From: Norway Posts: 35 Thanks: 0 How do I find out how much metal the container consists of? Hello, so I am stuck with a volume problem. A closed container which is shaped like a rectangular prism has the following measurments; Inside the container; 5,05 m x 2.45 m x 2.75 m Outside; 5.10 m x 2.50 m x 2.80 m Firstly, I had to find out how wide the walls of the container are and I did so by doing the following; 5/2 = 2.5 - I divided 5 by two because the the length and width on the inside of the container vs. length and width on the outside each equal 5 cm difference. I therefore divided it by two since we are talking about two sides. Know, I know I got the right answer, but is my way of thinking correct? Secondly, I was asked to find how much metal the container is built of. I thought they are asking about the perimeter, but I guess I'm wrong since I worked out the perimeter for the outerside of the container and got 83.2 m^3. The correct answer is 1.7 m^3. Could someone help me understand what method I am supposed to use/what they are asking for in mathematical terms?
October 7th, 2012, 08:19 AM   #2
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Re: How do I find out how much metal the container consists

Hello, mathismydoom!

Quote:
 A closed container which is shaped like a rectangular prism has the following measurments; Inside; 5,05 m x 2.45 m x 2.75 m Outside; 5.10 m x 2.50 m x 2.80 m Firstly . . . [snip] [color=blue]This is correct![/color] Secondly, I was asked to find how much metal the container is built of. I thought they are asking about the perimeter, but I guess I'm wrong [color=beige] .[/color][color=blue]Perimeter?[/color] since I worked out the perimeter for the outerside of the container and got 83.2 m^3. [color=blue]A perimeter is not measured in cubic meters.[/color] The correct answer is 1.7 m^3.

You said you were stuck with a "volume problem".
So why aren't you working with volumes?

$\begin{array}{cccc}\text{The volume of the entire box is: } & 5.10\,\times\,2.50\,\times\,2.80 \:=\:35.7\text{ m^3} \\ \\ \\

\text{The volume of inner space is: } & 5.05\,\times\,2.45\,\times\,2.75 \:=\:34.024375 \text{ m^3} \\ \\ \\

\text{The volume of metal is: } & 35.7\,-\,34.024375 \:=\:1.675625\text{ m^3} \end{array}$

$\text{The box is built of approximately }1.7\text{ cubic meters of metal.}$

October 8th, 2012, 01:21 AM   #3
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Re: How do I find out how much metal the container consists

Quote:
Originally Posted by soroban
Hello, mathismydoom!

Quote:
 A closed container which is shaped like a rectangular prism has the following measurments; Inside; 5,05 m x 2.45 m x 2.75 m Outside; 5.10 m x 2.50 m x 2.80 m Firstly . . . [snip] [color=blue]This is correct![/color] Secondly, I was asked to find how much metal the container is built of. I thought they are asking about the perimeter, but I guess I'm wrong [color=beige] .[/color][color=blue]Perimeter?[/color] since I worked out the perimeter for the outerside of the container and got 83.2 m^3. [color=blue]A perimeter is not measured in cubic meters.[/color] The correct answer is 1.7 m^3.

You said you were stuck with a "volume problem".
So why aren't you working with volumes?

$\begin{array}{cccc}\text{The volume of the entire box is: } & 5.10\,\times\,2.50\,\times\,2.80 \:=\:35.7\text{ m^3} \\ \\ \\

\text{The volume of inner space is: } & 5.05\,\times\,2.45\,\times\,2.75 \:=\:34.024375 \text{ m^3} \\ \\ \\

\text{The volume of metal is: } & 35.7\,-\,34.024375 \:=\:1.675625\text{ m^3} \end{array}$

$\text{The box is built of approximately }1.7\text{ cubic meters of metal.}$

I just have one more question which is what is the explanation as to why I have to find the volume for the inner and outer space in order to find out how much metal it consists of?

 October 8th, 2012, 01:28 AM #4 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 463 Math Focus: Calculus/ODEs Re: How do I find out how much metal the container consists The volume of the metal is the difference between the outer and inner volumes.
October 11th, 2012, 03:51 AM   #5
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Re: How do I find out how much metal the container consists

Quote:
 Originally Posted by MarkFL The volume of the metal is the difference between the outer and inner volumes.
Can I be a pain in the ass and ask you to formulate that in plain English? I worked out the surface of the container and of course I ended up with the wrong answer, but I don't understand why I'd have to use that method.

 October 11th, 2012, 04:27 AM #6 Global Moderator   Joined: Dec 2006 Posts: 18,421 Thanks: 1462 For a closed container (that has an empty interior), its overall (or "outer") volume comprises the volume of the material the container is made of and the volume of the empty interior of the container (its "inner" volume).

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