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### Course: MAP Recommended Practice>Unit 8

Lesson 7: Volume and surface area word problems

# Volume word problem: gold ring

See if you can find the incremental volume of a ring in cubic inches. You'll need to put to use your knowledge of how to measure volume. Created by Sal Khan.

## Want to join the conversation?

• why would the water move up that amount if there is a hole in the center of the ring? Wouldn't that hole fill up and change the amount of space the water takes up?
(8 votes)
• We are interested in the volume of the "gold". The hole in the ring fills up with water but the gold doesn't. So the water displaced by the ring is the volume of the gold
(22 votes)
• Wouldn't the volume of the ring be just 0.25 cubic inches? as the ring does not have a length of 3 inches and width of 2 inches?
(9 votes)
• The water level rises by 0.25 inches.
If you get 0.25 inches (height added) and multiply it by length and width (2 and 3) You get the total amount of water dispaced, which is the area of the ring. If you multiply your length times your width,(3x2) you get 6. 6 times 0.25 extra height =1.5 or *6 x 0.25 = 1.5
---Hopefully this makes it a little bit easier---
(5 votes)
• At , How come the inches in the water increase?
(4 votes)
• the ring's volume is 1.5, so it displaces the water so it stays even, Because atoms cant go inside of each other...
(4 votes)
• how to find area of box
(2 votes)
• A box is a 3D object, so you can either find the volume or the surface area, but there is no such thing as area of a 3D object.
(7 votes)
• So, basically, you can find the volume by finding the biggest object, then subtract the space that isn't the smaller object inside, right?
(5 votes)
• You take the volume after the item is put in subtract it from what it was before. That is how you get 1.5 cubic inches as the answer.
(1 vote)
• so you can know the ring's volume just like khan said at ?
(4 votes)
• Yea dude use the method he taught you in the video.
(2 votes)
• I have 2 questions. How could volume be in cubic inches? Why do you need to leave out the '4' in the height when solving for the mass of the ring?
(4 votes)
• Couldn't he just, like, find the volume of it by figuring out the volume of a cylinder?

It seems as if he could measure the height of the ring and the radius. Find the volume of that, then find the volume of the HOLLOW part the exact same way but subtracting the 'crust' from the diameter, then subtract? That seems more reasonable to me. Anyone know what I mean??
(3 votes)
• Ok, if a glass is filled within 5 inches high, 2.79, inches wide and 3.70 inches across. If I drop a ring and the height of the water goes to 7 inches, what is the volume of the ring?
(3 votes)
• 20.646, as u would multiply (7-5)*3.70*2.79, and get the result: 20.646.
(1 vote)
• Could we just have calculated both volumes and subtracted the answers together to find the volume of the gold ring
(2 votes)
• Well,if you mean taking the volume of the rectangular glass with the ring and subtract the volume of the rectangular glass without the ring, well you are right. Bang on!
(1 vote)

## Video transcript

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.