A solid aluminum sphere has a mass of 36 g. Use the density of aluminum to find the radius of the sphere in inches.

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hi everyone for this problem we want to find the radius of a nickel sphere and milliliters with a mass of g. So let's get started to calculate the radius of a sphere. We can use the formula for a volume of a sphere. And that formula is the volume of a sphere is equal to 4/3 pie. Are cute where V is our volume and our is our radius. So essentially we're trying to solve this are here. But before we can do that, we need to know what is our volume because that was not given. And we can calculate volume of a sphere using density and mass. So they gave us a mass of 110 grams and our equation for density is density is equal to mass over volume. This row here represents our density, R m is our mass and V is our volume because the problem tells us that we're working with nickel, we can look up the density of nickel and when we do that, the density of nickel is 8. grams per cubic centimeter. So if we isolate our density equation And we rearrange it to solve for volume, we'll get volume is equal to mass over density. And we have our mass 110 g and we have our density. So let's go ahead and solve for volume. So we have 100 and 10 g over 8.908 g per cubic centimeter. And if we pay attention to our units, we see that our grams cancel. And we're left with cubic centimeters which is the unit that we want for volume. So when you plug that into our calculator we will get a volume of 12. cubic centimeters. So let's go back to equation number one volume is equal to 4/ pi r. cute. So we have our volume and now we can solve for our radius. So let's go ahead and plug in. So our volume we said is 12. cubic centimeters Is equal to 4/3 pi r cubed. So let's simplify this a little bit. We get 12.35 cubic centimeters 4/3 times. Pi is four 189. And then we have are cute. We can divide both sides of our equation by 4.189. And when we do that we get are cute. Is equal to two 0.94 eight centimeters. Cute. Okay so now we need to take the cube root in order to isolate are are so if we take the cube root then we will have what looks like r. Is equal to the cube root of 2.94 eight. And because we're taking the cue group these will cancel. Okay So we'll take the cube root of 2.948. And you can also do this by raising 2.948 to the one third power. And when we do that calculation we'll get R. Is equal to 1. 34 centimeters. Now, the problem asked for it in middle leaders, so let's go ahead and do some unit conversion here. We want to go from cm two ml and one m. We have 100 cm And in one m There is 1000 milliliters. Okay, so let's look at our units here are centimeters cancel, our meters cancel and we're left with milliliters. So once we do this calculation we get are is equal to 14.3 four mellow millimeters. And this is our final answer. And that is the end of this problem. I hope this was helpful.

A solid aluminum sphere has a mass of 36 g. Use the density of aluminum to find the radius of the sphere in inches.

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Key Concepts

Density

Volume of a Sphere

Unit Conversion