Conversion of solids
Jamie wants to know the volume of his gold ring in cubic inches. He gets a rectangular glass with base 3 inches by 2 inches. So you see that here, the base is 3 inches by 2 inches. And he fills the glass 4 inches high with water. So you see that over here, 4 inches high with water. Jamie drops his gold ring in the glass and measures the new height of the water to be 4.25 inches. So this is after the gold ring is dropped. What is the volume of Jamie's ring in cubic inches? Well when you start with this water right over here and you add his ring, whatever that volume is of his ring is going to displace an equal volume of water and push it up. And so the incremental volume that you now have is essentially going to be the volume of his ring. Well what is the incremental volume here? Well it's going to be the volume. If you think about going from this before volume to the after volume, the difference is the base stays the same. It's 3 inches by 2 inches, the difference is-- to make it a little bit neater-- the base is the same. The difference is the height. The height now is 4.25 inches after dropping in the ring So the water went up by 0.25 inches. Let me write that, 0.25 inches is what the water went up by. So we could just think about, what is this incremental volume going to be? So this incremental volume right over here, that I'm shading in with purple. Well to figure that out we just have to measure. We just have to multiply the length times the width times the height times 0.25. So it's just going to be 3 times 2 times 0.25. 3 times 2 is 6, times 0.25, and you could do that either on paper or you might be able do that in your head. 4 times 0.25 is going to be 1, and you have 2 more times 0.25, that's going to be 0.5. So this is going to be 1.50. And we multiply it inches times inches times inches. So this is going to be in terms of cubic inches. 1.5 cubic inches is the volume of Jamie's ring, which is actually a pretty sizable volume for a gold ring. Maybe he has a very big finger or he just likes to spend, or I guess is his, whoever bought him the ring likes to spend a lot on gold.