Rolls of aluminum foil are 304 mm wide and 0.016 mm thick.
What m...

Question

Rolls of aluminum foil are 304 mm wide and 0.016 mm thick.
What maximum length of aluminum foil can be made from
1.10 kg of aluminum?

Accepted Answer

Hi everyone for this problem, we're told that engineers are creating roles of silver foil with a width of 430 and thickness of .012 mm. Using one kg of silver, we need to determine the maximum length in meters of silver foil that can be molded. Okay, so we need our density equation for this and our density equation is density is equal to mass over volume. And the first thing that we're going to want to do is calculate the volume of silver from the given mass and density of silver. So the density of silver is not given, but it is something that we can look up. And when we look it up, we see that the density of silver is equal to 10 0.49 grams per cubic centimeter. Okay, So if we're solving for volume to rearrange this equation to solve for volume, we're going to get volume is equal to mass over density. Okay, And so let's go ahead and solve for this are mass. We're told that we have one kg of silver. We need to convert this to grams. So in one kg There's 1000 g. Okay, so our kilograms cancel. And so we have a mass of g to plug in and then we have our density. Okay, so we have 1000 g over our density of 10.49 g per cubic centimeter, our grams cancel and we're left with unit of cubic centimeter, which is what we need for volume. And so we get a volume of 95.33 cubic cm. Now that we have our volume. We can isolate length by using this volume that we just calculated along with the given with and thickness. And the way we can do that is by using our thickness equation and our thickness equation tells us that thickness is equal to volume over area and remember our area is essentially length times width. And they give us our with Okay, and we need to solve for length. This is what the question is asking us for. It's asking us to determine the maximum length. So that length there is what we're going to solve for. Okay, so let's go ahead and plug in based off of what we know. So they give us our with and our thickness and mm. We need to convert this 2cm. So let's go ahead and do that first. Are with Is 430. And we need to convert this two cm. So and one m we have 1000 m 1000. And in one m We have cm. So this gives us a width of 43 cm and for a thickness we have zero point 012 mm and one meter there's millimeters. And in one m There's cm so we get a Thickness of 0. centimeters. Okay me move that over. So it's not cut off. So we have our width, we have our thickness and we have our volume. So we can go ahead and solve for our length here. Okay, so let's plug in what we know, We know that our thickness is 0.0012 cm is equal to our volume, which we calculated above 95.33 cubic centimeters over. And then we have length, which is what we're solving for Times with which is 43 cm. Okay, so now we need to simplify this so we can multiply both sides. Bye Length Times cm. And we'll multiply this. Bye length times 43 cm. Will multiply both sides by that. Okay. And so we'll get zero point 516 times length is equal to 95.33 cubic centimeters. So now we're going to divide both sides By 0.516. And when we do that we get I'm going to continue this over here. We get our length Is equal to 1,847 cm. But the question asked us for length in m. So we need to convert this to meters. In one m. We have 100 centimeters. Our centimeters cancel. And we're left with a length of 18.47 meters which is our final answer. That is the end of this problem. I hope this was helpful

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