# The Volume Of A Layer Of Lead Of Uniform Thickness(word problem)

• Plutonium88
In summary, the container is covered with a layer of lead shielding of uniform thickness. The volume of the shielding is a function of its thickness.
Plutonium88

## Homework Statement

A container in the form of a rectangular prism measuring 2m by 3m by 4m is covered with a layer of lead shielding of uniform thickness. Model the volume of the shielding as a function of its thickness. Treat the shelding as a hollow rectangular prism. DO NOT SIMPLIFY.

V=lxwxh

## The Attempt at a Solution

I found

l = 4m w = 3m h = 2m

when i drew each shape as a 2d shape. I noticed that the layer of lead was an equal (Uniform) layer around. So i labeled one unit of thickness, as t.

Thus all sides ended up having a layer on either side...

i came to conclude that the new measurements were.

L2=4 + 2t W2= 3 + 2t H2 = 2 + 2t

and since its hollow..

V(t) = L2*W2*H2 - Lwh

V(t) = (4+2t)(3+2t)(2+2t) - 4*3*2 <====(Or 24)

Can anyone tell me if this solution appears to be correct, and also point me out if I'm forgetting where any layers thickness maybe ?

Looks fine to me.

I think your answer looks good. I think you chose what your variable represented nicely and set up your function good. You can always check yourself in these situations to see if your answer makes sense. Does your equation make sense? In this case, the volume of the thickness should approach 0 as t approaches zero, and it does; so your equation seems reasonable.

Only "qualm" I would have is that you "found" l, h, and w. It would be better to let l, h, and w be the values they are, unless they specifically gave you equations for finding them. Just a little nitpick, I'm sure your teacher won't mind but it just makes it a little more rigorous.

But, again, for word problems there is usually a way to check and see if your solution makes sense. Let something get really small or really big and see if the answer makes sense, in this case it does!

scurty said:
I think your answer looks good. I think you chose what your variable represented nicely and set up your function good. You can always check yourself in these situations to see if your answer makes sense. Does your equation make sense? In this case, the volume of the thickness should approach 0 as t approaches zero, and it does; so your equation seems reasonable.

Only "qualm" I would have is that you "found" l, h, and w. It would be better to let l, h, and w be the values they are, unless they specifically gave you equations for finding them. Just a little nitpick, I'm sure your teacher won't mind but it just makes it a little more rigorous.

But, again, for word problems there is usually a way to check and see if your solution makes sense. Let something get really small or really big and see if the answer makes sense, in this case it does!

Thanks a lot guys i really appreciate it.

and so in terms of what you're saying with the approaching business.

i would know my answer shouldn't be correct if it was a negative number, cause volume can't be negative?

or like, can you explain to me a little more in depthly abuot the approaching bussiness and the equation.?

Plutonium88 said:
Thanks a lot guys i really appreciate it.

and so in terms of what you're saying with the approaching business.

i would know my answer shouldn't be correct if it was a negative number, cause volume can't be negative?

or like, can you explain to me a little more in depthly abuot the approaching bussiness and the equation.?

I'm not sure there's really much you need to check. It's a straighforward problem and you did it in a straightforward way. I really wouldn't worry about it.

Dick said:
I'm not sure there's really much you need to check. It's a straighforward problem and you did it in a straightforward way. I really wouldn't worry about it.

Yea you`re right no need to complicate things. I Really appreciate that you checked my answer and for your input man. It means a lot to me man keep up the great help man.

## What is the volume of a layer of lead with uniform thickness?

The volume of a layer of lead with uniform thickness can be calculated by multiplying the area of the base by the thickness of the layer. This can be represented as V = A x t, where V is the volume, A is the area, and t is the thickness.

## How do I find the area of the base in this word problem?

The area of the base can be found by using the formula for the area of a rectangle, which is length x width. In this problem, the base is likely a rectangular shape, so you would need to know the length and width of the layer of lead to find the area.

## Can I use any units of measurement to solve this problem?

Yes, you can use any units of measurement as long as they are consistent. For example, if the thickness of the layer is given in inches, then the area should also be in square inches. However, it is recommended to use the same units for both the thickness and the base to make the calculations easier.

## What if the layer of lead is not a perfect rectangle?

If the layer of lead is not a perfect rectangle, you can still use the same formula to find the volume. However, you may need to break the shape into smaller, more manageable rectangles and then add the volumes together to get the total volume.

## Is there a specific formula for calculating the volume of a layer of lead with uniform thickness?

Yes, the formula for the volume of a layer of lead with uniform thickness is V = A x t, where V is the volume, A is the area of the base, and t is the uniform thickness of the layer. This formula can also be applied to other shapes, as long as the thickness is consistent throughout the layer.

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