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### Course: Geometry 222-226 > Unit 1

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(20 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)

- At0:10, 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)

- 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)
- so you can know the ring's volume just like khan said at1:38?(4 votes)
- Yea dude use the method he taught you in the video.(2 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.(6 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)
- i found a wedding rind after watching this 🤣🤣🤣🤣🤣(3 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)

## 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.