A thief uses a can of sand to replace a solid gold cylinder that sits on a weight-sensitive, alarmed pedestal. The can of sand and the gold cylinder have exactly the same dimensions (length = 22 and radius = 3.8 cm). a. Calculate the mass of each cylinder (ignore the mass of the can itself). (density of gold = 19.3 g/cm³, density of sand = 3.00 g/cm³) b. Does the thief set off the alarm? Explain.

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Accepted Answer

Hey everyone. So here it says that thin cylinders are cut from a large cylinder. The density of the large cylinder is .98 g per cm cubed. It is 350 in diameter and one m in length. Under visual representation of this. Just think of a cylinder. Right? So here they're telling us the length is one m. So this is one m and the diameter Is 350. Now here it says how many thin cylinders can be cut from a large cylinder if each thin cylinder is .65 mm thick 350 in diameter. Also a follow up question, what is the mass of each thin cylinder? So think of us as slicing this cylinder? This tube into smaller pieces. Right? So and they're telling us that the diameter is still the same. And because I'm slicing it into smaller pieces, it's the link that's decreasing. So now it's .65 mm. Alright, so what we're gonna do here first is we're going to convert our .65 mm into meters. So remember here that one millim is 10 to the 93 m. So that comes out to .00065 m. Okay, and that's per cylinder here, per thin thin part. So we're gonna take our one m which is the length of the entire cylinder and divided by the length of one of these individual slices. When we do that. That gives me 1,538. That's the number of thin cylinder slices that we would get from cutting this larger long one m cylinder. So that means option c. Is our answer. Now, how would we find out the mass of each one though? Well we have the density of the large cylinder and we have enough information to help us to find the volume of a cylinder. Alright, so we're gonna say here that the volume of a cylinder which isn't given to us in the question but it's equal to pi times radius squared times height, peso pi times. Now remember Your diameter radius equals your diameter divided by two. So what do we have here? We have 350 millimeters And we divide that by two. Alright, so we divide that by two. That gives me 175 mm. And then I'm going to convert those mm into cm one cm is 10. So that's 17.5 cm for the radius. Okay. And multiply it by the centimeters of each individual slice. Because remember we're looking for the mass of an individual slice. So an individual slice is point 65 millimeters. And remember that one cm is equal to 10. So that's .065 cm. So that comes out to be 62.537 cm cubed. So it's the volume of a slice and it doesn't matter if I'm looking at a slice of the cylinder or the whole cylinder. The density is the density because it's unique to the material. So the density of even the slices still .98 g per cm cubed. So I'm gonna take the 62.537 cm cubed that I just found And it's .98 g per one cm cubed When I worked that out, that gives me 60 one point 28626 g here. The best answer Would be still see because it's the right number of slices, which is 1538 thin cylinders. Eat. The mask is a little bit off its 65 here, but it's actually closer to 61 g per thin cylinder. Giving us our final answer is option C.

Verified Solution

Key Concepts

Density

Volume of a Cylinder

Mass Comparison and Alarm Mechanism