Gold Brick.You win the lottery and decide to impress your friends by exhibiting a million-dollar cube of gold. At the time, gold is selling for $1282 per troy ounce, and 1.0000 troy ounce equals 31.1035 g. How tall would your million-dollar cube be?

Video transcript

Hey everyone. So in this problem we are working with density. So let's see what it's asking us. A science class is going to purchase $100 worth of silver at a cost of 1994 per ounce. It does give us the conversion between ounces and grams and the silver is going to be molded into a cube. And they're asking for the length of that cube with this amount of silver. So the first thing we're going to do is look at our density equation. So the density is the mass over the volume. And that's gonna help us figure out how we're gonna break down everything that they give us in this problem. So we don't have volume or sorry, they're not asking us for volume. They're asking us for length. We know it's a cube. So the volume of a cube recall is just the length cubed. We know that we have $100 worth of silver at this 1994 per ounce. So we're going to find the mass of the silver first. So we are given $100, you know it is one ounce or and they were nice enough to give us in the problem. This conversion rate of 28.35 g per outs Okay, so now we know that we are going to have For 142. g of silver. Alright, so we also need to recall the theoretical density of silver for this problem. It is 10. grams per centimeter cubed. That's just something that you'd have to look up. If this is on an exam, they would give this to you. Not something that you should memorize. All right. So from here we're going to use the density equation to solve or volume and then we'll use this volume equation to solve for the length. So volume is mass over density 142.18g, divided by 10.49 g per centimeter cubed gives us a volume of 13.55 cubic centimeters. And from there the length is the cube root of the volume. 13.55 cm two. That comes out to 2.38 cm. Look at our answer choices and we get answer. B. Alright, that's it. For this video. We'll see you guys in the next one.