Preserving the Catch!
Mr. Milette and Mr. Huang are going ice fishing this winter. They have a container to store their fish in. The container must be frozen completely with water the night before leaving for the fishing expedition, so that it thaws just in time to store some fish a few hours later. The rectangular container has a base of 9 cm by 11 cm and has a height of 38.5 cm. Assuming that water expands 10% when it freezes, determine the depth to which the container can be filled with water so that when it freezes, the ice does not go above the top of the container.
Hi there.
ReplyDeleteI think the depth to which the container can be filled with water is 34.65 cm. I thought of this answer by applying my knowledge of finding the volume and subtracting percents. First I identified the volume of the container. The volume is 3811.5 cm cubed. Since the water expands by 10% when it freezes, the water must be less than the total volume. To find 10% of the volume, I multiply the volume by 0.10, which is the volume of the water that when frozen, doesn't go over the container. So now that I have the volume of the water, I can also find the new depth.
Calculations:
9 x 11 x 38.5 = 3811.5 [VOLUME OF CONTAINER]
3811.5 x 0.10 = 381.15 [10% of VOLUME]
3811.5 - 381.15 = 3430.35 [VOLUME OF WATER TO NOT GO OVER CONTAINER]
3430.35 / 9 x 11 (99) = 34.65 [DEPTH]
Additionally, I could have just identified 10% of the height and subtract it to find the new depth
10% of 38.5 is 34.65. lol
goodbye (:
hey Jon
Deletethank you for your response~ seems fairly logical and clearly explained. You've discovered an interesting Math fact using the two methods; what is it?
The depth of the water in the container that when filled with water and freezes but does not go above the top of the container is 34.65 cm. The first thing that I did was find how much water that the container could hold. So, since the water expands by 10% when frozen, I knew that the water's depth had to be lower than the height of the container, 38.5 cm.
ReplyDeleteTo discover the height that the water should be was to find the volume of the container, which was 3811.5 cc (W x L x H). Then I found out what was 10% of 3811.5 cc which was 381.15 cc (3811.5 x 0.10). After doing this, I subtracted the volume of the container (3811.5) by 381.15 which was 3430.35 cc, the volume of the water.
Now that I had the volume of the water, 3430.35 cc, what I had to do next was find the depth of the water. To get the depth, I remembered the process of finding the volume, and now that I had the volume I decided to reverse the process : 3430.35 / (W x L )
So when I reversed the process I knew that the answer would have to be the height of the water. The answer I got was 34.65 cm, which is the amount of water the container has to be filled up.
-Rachel
hi Rachel thank you for responding to this challenge! Some people may ask you what you meant by 'reversing' the process. How would you explain this?
Deleteice fishing? sounds fun! I am in!
ReplyDeleteLooking forward to reading your input in the coming week! Remember: it's okay to utilize any resources you can gather to help you solve this problem.
First, I figured out the volume; l*w. That meant I multiply 9 by 11. That is the area of the rectangular bottom of the container. Then, to figure out the volume, I multiply by 38.5; getting 3811.5 cm3. After that, I figured out the amount of water, in cubic centimetres, which involved getting 10% of 3811.5 cm3, thereby getting 381.15 cm3 in water. In mL, you would need 381.15 mL of water, or about 3.85 cm of water tall.
ReplyDeleteAaron thanks for stopping by and chipping in your two cents~ =)
DeleteI like how you relate the units (science!); however, I am uncertain as to how you can go from 381ml to 3.8 cm. Can you show us how?
Most people thought to get 10% of 3811.5 than subtract it, but then 10% of the difference will not add up to 3811.5. So after trial and error, the answer i got was 3465 ml or filled up to 35 cm.
ReplyDeleteHi Matt Thanks for responding! What do you mean by '10% of the difference will not add up to 3811.5"? Can you show us your process? Thanks.
DeleteHello
ReplyDeleteSo I think that the depth in which the water can be filled up to it 34.65.
CALCULATIONS
Step 1: Find the volume-------> area of base x height(9 x 11 x 38.5= 3811.5)
Step 2: Find 10% of the volume------> 3811.5 x 0.10 = 381.15 - 3811.5= 3430.35
Therefore 10 % of the volume is 3430.35
Step 3: Working backwards to find the depth
3430.35/99(base of container)= 34.65
Therefore the depth is 34.65
Bye
hi Shalindree~
Deletethanks for responding to this post. Your process seems logical; Can you check step 2 when you subtract a larger amount from a smaller amount? you know me, I am all about laying out the process as clearly as possible, especially when it comes to proper math expression/equations~ =)
Oops, made a silly mistake
DeleteThe numbers are actually supposed to be switched. So the subtraction sentence is actually 3811.5-381.15=3430.35
HI!
ReplyDeleteI think that the depth that the water can be filled up to is 34.65.
First, I found the volume of the container.
To find the volume I did 9 x 11 x 38.5 (L x W x H)
L x W x H
=9 x 11
=99 x 38.5
=3811.5
Then, since I know that the water will freeze up to 10% , I have to find 10% of 3811.5. The word "OF" tells me I have to multiply the 2 numbers to get the number I have to subtract. I know this because I used the knowledge of finding tax from last year.
3811.5 x 0.10 (10%) = 381.15 ( the number I have to subtract)
Now I will subtract the volume of the container (3811.5) and the expansion of the water (381.15)to find out the volume of the water.
3811.5 - 381.15 = 3430.35 (volume of water)
Now that I have found the volume of the water I have to find the depth of the water. I will have to divide the volume of the water (3430.35) with the base area (L x W) (9 x 11 = 99). Which is working backwards.
3430.35 / 99 = 34.65
So, the depth in which the container can be filled up to is 34.65.
Thanks for reading Bye!
- Kajana
Thank you Kajana for your response~ =) You've explained your rationale clearly and I am convinced! (Well, what is the unit of the final answer?)
DeleteHey
DeleteThe unit of the final answer will be cm because the container is measured in centimeters. So the final answer will be 34.65cm.
Good job Kajana. Good job explaining.
DeleteHey peeps,
ReplyDeleteAs I was gathering up my assumptions, methods and solutions, the depth of the container is 34.65 cm.
My first method was that basically and apparently the height of the original container was the depth, therefore we have to identify the new depth after the expansion. I basically multiplied 10% to the original depth first.
1. 38.5cm*0.10= 3.85 cm
Then I simpily subtracted it from the original height and that is the new depth.
38.5-3.85= 35.65cm
My second method of this question was...
Delete1. First I found the volume of the original container:
Volume= 9*11*38.5= 3811.5 cm
The volume of the original container was 3811.5cm cubed.
2. Then I found the expansion volume after multiplying the 10% expansion.
3811.5*0.10= 381.15cm
3. Then I subtracted this from the original container's volume.
3811,5-381.15= 3430.35cm
4. Now I worked backwards by doing the whole equation for volume backwards. BASICALLY I dived the amount with the base are of the original volume.
3430.35/99 (11*9)= 34.65 cm.
The new depth is 34.65 cm
Great work, great sharing, and excellent questions. Find below the provided answer:
ReplyDeleteSolution 1
To determine the volume of a rectangular solid, multiply the length, width and height. So the
maximum volume of the container will be
9 x 11 x 38.5 = 3811.5 cm3
Let the original depth of water in the container be h cm.
Then the water volume before freezing is 9 x11 x h = (99 x h) cm3. After the water freezes, the
volume increases by 10% to 110% of its current volume. So after freezing, the volume will be
110% of 99 x h = 1.1 x 99 x h = (108.9 x h) cm3
But the volume after freezing is the maximum volume, 3811.5 cm3. Therefore,
108.9 x h = 3811.5 and it follows that h = 3811.5 x 108.9 = 35 cm.
The container can be filled with water to a depth of 35 cm so that when it freezes the ice will
not go over the top of the container.
Solution 2
In this solution we note that the length and width remain the same in both the volume
calculation before and after the water freezes. We need only concern ourselves with the change
in the depth of the water.
Let the original depth of water in the container be h cm.
After freezing, the depth increases by 10% to 110% of its depth before freezing. So after
freezing, the depth will be 110% of h = 1.1 x h = 38.5 cm, the maximum height of the
container. Then h = 38.5 x 1.1 = 35 cm.
The container can be filled with water to a depth of 35 cm so that when it freezes the ice will
not go over the top of the container.
hi :)
ReplyDelete