Problem

What is the density of lithium metal in g/cm3 if a cylindrical wire with a diameter of 2.40 mm and a length of 15.0 cm has a mass of 0.3624 g?

Relevant Solution
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Hey everyone for this problem we're being asked to calculate the density of brass and g per cubic centimeter. If a brass cylinder has a length of 2.32 cm, a radius of 1.02 cm and a mass of 65.49 g. So let's get started. The formula for calculating density is density is equal to mass over volume. And this symbol row here represents density and they specifically asked us for it in the unit of grams per cubic centimeter. Density can also be represented in grams per milliliter. But here we're calculating it in grams per cubic centimeter. So that means our mass needs to be in grams and our volume needs to be in cubic centimeters. So let's get started with our numerator, we know that our mass Is given and it is 65.49g. So there's nothing we need to do further here. They gave it to us in g which is perfect for our volume. We're told that we have a brass cylinder and the volume of a cylinder can be calculated using the formula pi r squared times H where r is our radius and H is our height. They tell us we have a radius of 1.2 centimeters and a length of 2.32 centimeters. Our length is the same thing as height. So once we plug those values in we'll know what our value is for volume. So let's go ahead and do that now. So we have pie Times our radius of 1. centimeters squared times our height of 2. centimeters. Okay, so once we calculate that we'll get a volume of seven 58 cm cubed. And so we see here we have a squared and then This can be represented by one. And so we'll get cubed as the final unit, which is what we need for our volume. So we have everything we need to plug in. So let's go ahead and plug those values in. We have a mass of 65 0. grams and we have a volume of 7. eight cubic centimeters. Once we plug that into our calculator, we're going to get a density of 8. grams per cubic centimeter. And this is our final answer. This is their density of brass. If the cylinder had the following length, radius and mass, that's the end of this problem. I hope this was helpful.