The next POTW (#6) is below. Please remember to reply and comment to your peers.
Thursday, October 23, 2014
Math POTW #6 - Reach for the Top
Last week's POTW was seemingly "easy" as many people obtained the correct answer of $14.30. HOWEVER, we really wanted students to also try and solve the problem algebraically. Please see below for how that might be done. Do you understand how it is solved in this way?
The next POTW (#6) is below. Please remember to reply and comment to your peers.
The next POTW (#6) is below. Please remember to reply and comment to your peers.
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First we need to find the volume of the big storage tank (4x4x5=80m³). Then, I want to find the volume of the water and the cube separately (Water: 2.5x4x4=40m³)(Cube: 2x2x2=8m³). So we have 40m³ water in a 80m³ storage then add 8m³ to the 40m³ and get 48m³ (40+8). Because to reach the top we need at least 80m³ of water and only have 48m³ we can't reach the top and have 32m³ needed to reach it.
ReplyDeletefirst you find the volume of the tank or the capacity which is 4x4x5 or 80, next you find the volume of the water or 4x4x2.5 or 50. then you find the cube's volume which is 2 cubed or 2x2x2 which is 8. all you have to do is add 8 to 50, that is the volume of the water with the cube, 58 is less than 80 and is 22 away from 80, so it is less that the top and 22 away from the top.
ReplyDeleteVolume of tank: 5x4x4=80m cubed
ReplyDeleteVolume of amount of water in the tank: 2.5x4x4x=40m cubed
Volume of the block being placed: 2x2x2=8m cubed
8m cubed+40m cubed=48m cubed
No it will not fill the tank.
The water will rise to 3m high therefore 5m-3m=2m meaning that the water be 2m below the top of the tank
First I have to find the volume of the storage tank, then the volume of the tank that is already filled, and the volume of the cube. Then, I will add the volume of the cube to the water already in the tank and see if it exceeds the total volume of the tank. The formula to find the volume is height times base times width. The storage tank can hold 4x4x5=80m cubed. The volume of the water is 4x4x2.5=40m cubed. The volume of the cube is 2x2x2=8m cubed. The volume of the water and the cube together is 40+8=48m cubed. 48m cubed is now in the 80m cubed tank. 48m cubed<80m cubed, the water will not overflow and there will still be 32m cubed of space in the tank left. 80m cubed-48m cubed=32 m cubed
ReplyDeleteFirst of all, we know that the rectangular prism is 4x4x5 so the volume is 80m^3 if you mulitply each length. If you put water that fills the tub by 2.5 heigh, it is half the volume of the tub as the total height is 5m and 5/2=2.5. Therefore, it takes up 80/2=40m^2. Now the, the tank is 40 out of 80 metres cubed full. It states that a 2x2x2 cube is thrown into the tank so the volume is 8m^3. If you add the 8m^3 by 40m^3, the water will raise by 8m^3 which means it will raise by 0.5m. I know this because the base with a 1cm high height 4x4 which is 16m^3 and half 16 is 8 which is the volume of the small cube so half of 1m is 0.5m. Therefore, the water is not close to full as it only raises by 10% or 0.5m/5m. With the water, it is 2.5m+0.5m which is 3m/5m or 60% full.
ReplyDeleteto solve this question, I first found out the volume the tank, water and cube.
ReplyDeleteTank: 5x4x4=80m cubed
water: 2.5x4x4=40m cubed (water filled halfway up the container)
cube: 2x2x2=8m cubed
then I added 8m cubed(volume of cube) to 40m cubed( volume of water) and got 48m cube which was the waters level once the cube was added. Lastly, I subtracted 48m cubed from 80m cubed (volume of tank) and got 32m cubed which is how far blow the top the water reaches
The answer is that we will not reach the top and there will be 32 meters cubed to reach the top. To find this, I first needed to find the volume of the container which I did by multiplying width x length x hight ( 4x4x5=80 meters cubed.) Next I found the volume of water as well as the volume of the cube separate:
ReplyDeleteCube: 2x2x2= 8 meters cubed
Water: 2.5x4x4= 40 meters cubed
I then added 8 to 40 and received 48 followed by a subtraction from 80 receiving an answer of 32 meters cubed