Volume of an Irregular Object

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geekily

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The volume of an object with an irregular shape can be determined by measuring the volume of water it displaces.

a. A rock placed in an aquarium measuring 2.5 feet long by 1 foot wide causes the water to rise 0.25 inches. What is the volume of the rock?

b. With the rock in place, the water level in the aquarium is 0.5 inches from the top. The owner wants to add to the aquarium 200 solid marbles, each with a diameter of 1.5 cm. Will the addition of these marbles cause the water in the aquarium to overflow?

I actually checked several times to make sure I was doing the right page, because my teacher never mentioned anything about what to do to find the volume of irregular objects, and I haven't been able to find anything about it in the book, either - though even she admits that the book descriptions are more confusing than helpful. I thought I'd start off by taking the surface area of the tank, but I only have 2 dimensions of the tank, so I can't. I have no idea where to start with this one. Can someone please give me a push in the right direction? It seems like a lot of the other problems are like this, too, so until I can figure out this concept, I'm kind of stuck. Thanks!

I'm sorry, I forgot to say that the answer key says the answer to part a is 90 in^3 and part b is no.
 
a. If you place a rock in a tank with a water level that you measured and you know how much the water level has risen, what does the difference between the second and first measurement tell you?

b. If you understand what's happening in a, you probably get the idea when you add more 'irregular shapes' into the tank.
 
Well, I think the rise in water level would tell you the weight of the rock in relation to the water, but I don't know what that would be or how to find it from that.
 
a. A rock placed in an aquarium measuring 2.5 feet long by 1 foot wide causes the water to rise 0.25 inches. What is the volume of the rock?

I would convert to inches. Just picture a rectangular solid measuring 2.5 feet by 1 ft by .25 inches. That volume is equivalent to the volume of the rock. If you want the answer in cubic inches, it will be 0.25 x 2.5 x 12 x 1 x 12 cubic inches.
If you want it in cubic feet it will be 0.25/12 x 2.5 x 1 cubic feet.
 
geekily said:
The volume of an object with an irregular shape can be determined by measuring the volume of water it displaces.

a. A rock placed in an aquarium measuring 2.5 feet long by 1 foot wide causes the water to rise 0.25 inches. What is the volume of the rock?

b. With the rock in place, the water level in the aquarium is 0.5 inches from the top. The owner wants to add to the aquarium 200 solid marbles, each with a diameter of 1.5 cm. Will the addition of these marbles cause the water in the aquarium to overflow?

I actually checked several times to make sure I was doing the right page, because my teacher never mentioned anything about what to do to find the volume of irregular objects, and I haven't been able to find anything about it in the book, either - though even she admits that the book descriptions are more confusing than helpful. I thought I'd start off by taking the surface area of the tank, but I only have 2 dimensions of the tank, so I can't. I have no idea where to start with this one. Can someone please give me a push in the right direction? It seems like a lot of the other problems are like this, too, so until I can figure out this concept, I'm kind of stuck. Thanks!

I'm sorry, I forgot to say that the answer key says the answer to part a is 90 in^3 and part b is no.
Click to expand...

This is one of the better-known ways to find the volume of an irregular object. Put the object into a container of water. The volume of the water displaced is the volume of the rock.

When you put the rock into an aquarium that is 2.5 feet long and 1 foot wide, the level of the water rises 0.25 inches. The volume of water displaced, then is the volume of a rectangular prism with length 2.5 feet, width 1 foot, and height 0.25 inches.

Change everything to inches, then find the volume.

V = 30 inches *12 inches * 0.25 inches
V = (30 * 12 * 0.25) in^3
V = 90 in^3

For part b, find the volume of one marble. It's a sphere, and for a sphere,
V = (4/3) pi r^3

The diameter is 1.5 cm. Find the radius, and substitute into the volume formula.

Now, you are going to add 200 marbles. Multiply the volume of one marble to find the total volume of all the marbles.

According to the problem statement, if the water in the aquarium rises more than 0.5 inches, the aquarium will overflow. That is, if the total volume of the marbles (careful, this will be in cm^3!!) is greater than the volume of a rectangular prism with length 2.5 feet, width 1 foot, and height 0.5 in. You'll need to calculate this volume in cm^3.....compare with the total volume of the marbles. If the volume of the marbles is greater than the volume of the rectangular prism, the water will overflow.

I hope this helps you.
 
Oh, okay, that's what I was unclear on - that the volume of water displaced was actually equal to the volume of the rock. Thank you so much! The rest of it made sense to me. For part b, I wound up with 200 marbles having a volume of 21.56757144 in^3, and the aquarium having a volume of 180 cm^3.

Thanks so much for explaining this! It really helped.
 
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