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IH neres priceyl] caeasie 2o8-earatsc of W 8 pts) 3 the mass volume_ diamonds cubic often telimecessreaf...

Question

IH neres priceyl] caeasie 2o8-earatsc of W 8 pts) 3 the mass volume_ diamonds cubic often telimecessreaf

IH neres priceyl] caeasie 2o8-earatsc of W 8 pts) 3 the mass volume_ diamonds cubic often telimecessreaf



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Diamond has a density of $3.513 \mathrm{g} / \mathrm{cm}^{3} .$ The mass of diamonds is often measured in "carats," where 1 carat equals $0.200 \mathrm{g} .$ What is the volume (in cubic centimeters) of a 1.50 -carat diamond?

So for this problem, we have a diamond with a known mass kind of the masses and carrots those. It's not really a mass that we're familiar with, but we do know a conversion between carrots and grams. We can use that to get to a mass there were more familiar with. Ultimately, we're trying to get to a volume that so let's try starting out with our five 0.0 carats where the abbreviation for that a c t. We're then going to go to grams using the given conversion factor of one carrot is 0.2 Corey Ems. There we go. Ah, and now that we're in, units of grams were still. Check that by cancelling units here. Good marine units of grams. Let's go ahead and use the given density of diamond to convert to a volume. So that's 3.51 grams. 21 cubic centimeter. Again, let's check units, grams grams leaving us with Centimeters Cube. That's good, because we wanted a volume at the end of the day, and so this is going to be equal to zero 0.28 five centimetres. Who put me? We try and make a little bit more room for that centimetres cubed

Okay when Current? Because 0.200 Graham Density of diamond is three for 51 gram per cubic centimeter. So if you have a five carat diamond and we're looking for a bawling and bawling, put the coach Fulham Eco's to mass over density on. We have to convert the mass from carrot to Graham because of the unit of Density. So it's gonna be five times 0.200 Divide by three or 51 the product of cereal from 28 mil. Leader. If you have 2.8 mil Leader Diamond or just the mess in because the time D and, uh, the product of this will be in grand and we'll eat the unit that the question as a scared. So we have Thio. Divide that number advisable trying to, so it will be 2.8 Time 3.51 Do you ride it by zero. Fine, too. And the product of that is for the night carrots

This problem discusses the kohinoor diamond, some measurements and some factoids, and we'll do some calculations. I hope I'm pronouncing it right. Were given a part meat. The density of diamonds Is taken as 3.51 grams per cubic centimeter. We are told that the corner Diamond is 108 carats. And we are given the Equality that one carrot is equal to 2.00 Times 10 to the Second Milligrams or 200 mg. We are asked to sell for two things first, the mass of the diamond in pounds and second, the volume and inches cubed. Okay, let's get started. We're going to set up our first problem. I'm just going to go through and set it up quickly for you. It's not too difficult. We'll start with our 108 carats. 108 carats. Using this equality, we can convert carrot two mg. We can convert milligrams, two g Using one g is 1000 mg. And I looked up at £1,, has a mess of 453 0.6 g, switch colours and we will go ahead and cross out everything that cancels carrots cancelled. Milligrams, cancel in grams, cancel. We put in our math our numbers into a calculator And report to the correct number of significant figures. We get 0.0 47 six pounds for part A for part B. Again, we're going to start with 108 carrots. We're gonna do the same conversions 2.00 Times 10 to the Second Milligrams is one carrot. Again, we use the same conversion factor to go from milligrams to grams. And now I'm going to use our density Which is one cm Cube has a mass of 3.51 g. And finally I'm going to use 2.54 cm equals one inch. Now, what's important is I have to cube this entire quantity and remember, I don't need to just cube the centimeters I need to. This will be 2.54 cubed and centimeters cubed. I've already done the math on this and I got 0.376 cubic inches. Problem solved.

In this case in distribution we have volume, volume equals two 1.84 cubic inch. And we know that one inch Equals to 0.02 54 m. So one INGE Q Equals to one 68 we take you into tends to the power minus five. So According to this, in 1.84 cubic inch equals two 30.2-10 to the power -6 me Turkey. So this is our mm answer for this question and this answer giving off a hands. What option? A? It's correct. Okay, thank you.


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