#$&* course PHY 122 9/4 3pm If your solution to stated problem does not match the given solution, you should self-critique per instructions at
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Given Solution: `aThe volume of the container is 10 cm * 10 cm * 10 cm = 1000 cm^3. So it would take 1000 cubic centimeters of fluid to fill the container. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique rating #$&*OK ********************************************* Question: `q002. How many cubes each 10 cm on a side would it take to build a solid cube one meter on a side? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: It takes 100 cm to make 1 meter. So to make a 1 meter side it would take 10-10cm blocks. confidence rating #$&*3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `aIt takes ten 10 cm cubes laid side by side to make a row 1 meter long or a tower 1 meter high. It should therefore be clear that the large cube could be built using 10 layers, each consisting of 10 rows of 10 small cubes. This would require 10 * 10 * 10 = 1000 of the smaller cubes. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique rating #$&*OK ********************************************* Question: `q003. How many square tiles each one meter on each side would it take to cover a square one km on the side? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: 1 km equals 1000 meters. So it would take 1000-one meter square tiles to cover 1 km square tiles. confidence rating #$&*3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `aIt takes 1000 meters to make a kilometer (km). To cover a square 1 km on a side would take 1000 rows each with 1000 such tiles to cover 1 square km. It therefore would take 1000 * 1000 = 1,000,000 squares each 1 m on a side to cover a square one km on a side. We can also calculate this formally. Since 1 km = 1000 meters, a square km is (1 km)^2 = (1000 m)^2 = 1,000,000 m^2. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique rating #$&*OK ********************************************* Question: `q004. How many cubic centimeters are there in a liter? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: There are 1000cm^3 in a liter. confidence rating #$&*2 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `aA liter is the volume of a cube 10 cm on a side. Such a cube has volume 10 cm * 10 cm * 10 cm = 1000 cm^3. There are thus 1000 cubic centimeters in a liter. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique rating #$&*OK ********************************************* Question: `q005. How many liters are there in a cubic meter? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: If there is 1000cm^3 in a liter then there is 10 meter^3 in a liter. 10 meters^3 equals 1000cm^3. confidence rating #$&*3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `aA liter is the volume of a cube 10 cm on a side. It would take 10 layers each of 10 rows each of 10 such cubes to fill a cube 1 meter on a side. There are thus 10 * 10 * 10 = 1000 liters in a cubic meter. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique rating #$&*OK ********************************************* Question: `q006. How many cm^3 are there in a cubic meter? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: The prefix cm equals .01 so there are .01meters^3 in cm^3. So there are 100 cm^3 in a cubic meter. confidence rating #$&*3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `aThere are 1000 cm^3 in a liter and 1000 liters in a m^3, so there are 1000 * 1000 = 1,000,000 cm^3 in a m^3. It's important to understand the 'chain' of units in the previous problem, from cm^3 to liters to m^3. However another way to get the desired result is also important: There are 100 cm in a meter, so 1 m^3 = (1 m)^3 = (100 cm)^3 = 1,000,000 cm^3. STUDENT COMMENT It took me a while to decipher this one out, but I finally connected the liters to cm^3 and m^3. I should have calculated it by just converting units, it would have been easier. INSTRUCTOR RESPONSE The point isn't just conversion. There are two points to understanding the picture. One is economy of memory: it's easier to remember the picture than the conversion factors, which can easily be confused. The other is conceptual/visual: the picture gives you a deeper understanding of the units. In the long run it's easier to remember that a liter is a 10-cm cube, and a cubic meter is a 100-cm cube. Once you get this image in your mind, it's obvious how 10 layers of 10 rows of 10 one-cm cubes forms a liter, and 10 layers of 10 rows of 10 one-liter cubes forms a cubic meter. Once you understand this, rather than having a meaningless conversion number you have a picture that not only gives you the conversion, but can be used to visualize the meanings of the units and how they are applied to a variety of problems and situations. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): I didn't visualize the litter euqal to 10-cm cube equals 100-cm cube. I only did the conversion for units. It does become clearer when you visualize the problem. ------------------------------------------------ Self-critique rating #$&* ********************************************* Question: `q007. If a liter of water has a mass of 1 kg the what is the mass of a cubic meter of water? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: A liter equals 10 meter^3 and it is given that 1kg of water has a mass of 1kg. Then if the each of 10 1x1x1 meter blocks would have a mass of 1kg/10 which would equal .1 kg. confidence rating #$&*3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: Since there are 1000 liters in a cubic meter, the mass of a cubic meter of water will be 1000 kg. This is a little over a ton. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): I got caught up in the conversion factors. I drew out the pitchure and did the problem completly wrong. I understand that if there are 1000L in a m^3 and 1l has a mass of 1kg that 1m will have a mass of 1000kg. I just need more practice with these sorts problems so they will be clearer when i solve them. ------------------------------------------------ Self-critique rating #$&* ********************************************* Question: `q008. What is the mass of a cubic km of water? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: If the density of the water was know the mass could be caculated but without that information I have no real answer. confidence rating #$&*0 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `aA cubic meter of water has a mass of 1000 kg. A cubic km is (1000 m)^3 = 1,000,000,000 m^3, so a cubic km will have a mass of 1,000,000,000 m^3 * 1000 kg / m^3 = 1,000,000,000,000 kg. In scientific notation we would say that 1 m^3 has a mass of 10^3 kg, a cubic km is (10^3 m)^3 = 10^9 m^3, so a cubic km has mass (10^9 m^3) * 1000 kg / m^3 = 10^12 kg. STUDENT QUESTION I don’t understand why you multiplied the 1,000,000,000 m^3 by 1000 km/m^3. I also don’t understand where the (1000m)^3 came from. I thought I had this problem but it stumped me. It is probably something really simple that I am missing. ??? INSTRUCTOR RESPONSE A km is 1000 meters, but a cubic km is a cube 1000 meters on a side. It would take 1000 m^3 just to make a single row of 1-m cubes 1000 meters long, and you would hardly have begun constructing a cubic kilometer. You would need 1000 such rows just to cover a 1-km square 1 meter deep, and 1000 equal layers to build a cube 1 km high. Each layer would require 1000 * 1000 cubic meters, and 1000 layers would require 1000 times this many 1-meter cubes. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): I am a little confused about how the cubic meter of water has a mass of 1000 kg, but the rest is very clear of how it takes 1000 rows, of 1000 blocks that would go 1000 heigh to get the final answer. ------------------------------------------------ Self-critique rating #$&* ********************************************* Question: `q009. If each of 5 billion people drink two liters of water per day then how long would it take these people to drink a cubic km of water? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: It would take 1000 1 meter square blocks per row of 1000 rows and a 1000 block heigh to make a cubic km. There are 1000 liters in a meter^3 so there for the amout of water needed to drink would be 1*10^9*1000 which would be 1*10^12 of liters of water that need to be drank. The water is being consumed at 2 liters per day by 5 billion people. So (1*10^12)/(5*10^9*2)=100days. confidence rating #$&*3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a5 billion people drinking 2 liters per day would consume 10 billion, or 10,000,000,000, or 10^10 liters per day. A cubic km is (10^3 m)^3 = 10^9 m^3 and each m^3 is 1000 liters, so a cubic km is 10^9 m^3 * 10^3 liters / m^3 = 10^12 liters, or 1,000,000,000,000 liters. At 10^10 liters per day the time required to consume a cubic km would be time to consume 1 km^3 = 10^12 liters / (10^10 liters / day) = 10^2 days, or 100 days. This calculation could also be written out: 1,000,000,000,000 liters / (10,000,000,000 liters / day) = 100 days. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique rating #$&*OK ********************************************* Question: `q010. The radius of the Earth is approximately 6400 kilometers. What is the surface area of the Earth? If the surface of the Earth was covered to a depth of 2 km with water that what would be the approximate volume of all this water? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: Surface area of a sphere can be found by 4*pi*r^2 which equals 4*pi*(6400km)^2 which equals 5.14719*10^8 km^2. If the surface area was cover with 2km of water the volume of this water could be found be subtacting the original surface area by the new surface area that was formed by the 2 km of water. Original surface area of earth would be (4/3*)*pi*(6400km)^3 or 1.09807*10^12 km^3, the new volume with the added water would be (4/3)*pi*(6402 km)^3 or 1.0991*10^12 km^3. By subtracting the two the total vollume of 1.09807*10^12 km^3-1.0991*10^12 km^3 which is 1.02976*10^9 km^3 would be found. confidence rating #$&*3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `aThe surface area would be A = 4 pi r^2 = 4 pi ( 6400 km)^2 = 510,000,000 km^2. A flat area of 510,000,000 km^2 covered to a depth of 2 km would indicate a volume of V = A * h = 510,000,000 km^2 * 2 km = 1,020,000,000 km^3. However the Earth's surface is curved, not flat. The outside of the 2 km covering of water would have a radius 2 km greater than that of the Earth, and therefore a greater surface area. However a difference of 2 km in 6400 km will change the area by only a fraction of one percent, so the rounded result 1,020,000,000,000 km^3 would still be accurate. STUDENT COMMENT I thought that in general pi was always supposed to be expressed as pi when not asked for an approximate value so in the first part of the problem I didn’t calculate pi. For the second part of the question I assumed approximate meant calculate pi into the equation which would still be a less precise answer so I did not round any further. ???Should I have estimated more than I did??? INSTRUCTOR RESPONSE The given information says 'approximately 6400 km'. Your result, 163,840,000pi km^2, is perfectly fine. However most people aren't going to recognize 163,840,000 as 4 times the square of 6400 (unlike a result like 36 pi (easily enough seen as either 6^2 * pi, or 4 * 3^2 * pi)). Since the given information is accurate to only a couple of significant figures, there's no real advantage in the multiple-of-pi expression. In the given solution the results are generally expressed to 2 significant figures, consistent with the 2 significant figures in the given 6400 km radius. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique rating #$&*OK ********************************************* Question: `q011. Summary Question 1: How can we visualize the number of cubic centimeters in a liter? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: There are 1000 cm^3 in a liter, so we can visulize that there are 10 1cm blocks in a row that have 10 rows and have a height of 10 blocks heigh for a total of 1000 1cm blocks. confidence rating #$&*3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: Since a liter is a cube 10 cm on a side, we visualize 10 layers each of 10 rows each of 10 one-centimeter cubes, for a total of 1000 1-cm cubes. There are 1000 cubic cm in a liter. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique rating #$&*OK ********************************************* Question: `q012. Summary Question 2: How can we visualize the number of liters in a cubic meter? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: If we know that 1l equals 1000cm^3 we then can say that (1m)^3 equals (100cm)^3 and say that 1m^3 equals 1,000,000cm^3. Then we could say that in order to make 1,000,000cm^3 it would take 1000 times that amount to make a meter^3 and there for m^3 would equal 1000L. Or that it would take 10 units deep, 10 across, and 10 heigh to make the difference for a total of 100. confidence rating #$&*3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: Since a liter is a cube 10 cm on a side, we need 10 such cubes to span 1 meter. So we visualize 10 layers each of 10 rows each of 10 ten-centimeter cubes, for a total of 1000 10-cm cubes. Again each 10-cm cube is a liter, so there are 1000 liters in a cubic meter. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique rating #$&*OK ********************************************* Question: `q013. Summary Question 3: How can we calculate the number of cubic centimeters in a cubic meter? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: (1m)^3=(100cm)^3 1m^3=1000000cm^3 confidence rating #$&*3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `aOne way is to know that there are 1000 liters in a cubic meters, and 1000 cubic centimeters in a cubic meter, giving us 1000 * 1000 = 1,000,000 cubic centimeters in a cubic meter. Another is to know that it takes 100 cm to make a meter, so that a cubic meter is (100 cm)^3 = 1,000,000 cm^3. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique rating #$&*OK ********************************************* Question: `q014. Summary Question 4: There are 1000 meters in a kilometer. So why aren't there 1000 cubic meters in a cubic kilometer? Or are there? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: 1000 cubic meters implies overall will be 1000 cubic meters overall would result from a 10 x 10 x10 meter block. A cubic kilometer is a cube that is 1k x 1k x 1k which is much larger than 1000 cubic meters. confidence rating #$&*3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `aA cubic kilometer is a cube 1000 meters on a side, which would require 1000 layers each of 1000 rows each of 1000 one-meter cubes to fill. So there are 1000 * 1000 * 1000 = 1,000,000,000 cubic meters in a cubic kilometer. Alternatively, (1 km)^3 = (10^3 m)^3 = 10^9 m^3, not 1000 m^3. STUDENT ANSWER to question: Because a cubic kilometer is cubed. A regular kilometer is not going to contain as much as a cubic kilometer. INSTRUCTOR RESPONSE Kilometers and cubic kilometers don't measure the same sort of thing, so they can't be compared at all. Kilometers measure distance, how far it is between two points. Cubic kilometers measure volume, how much space there is inside of something (there is space, though not necessarily empty space, inside of any container or any 3-dimensional region, whether it's full of other stuff or not. If it's full of other stuff then we wouldn't say that it's 'empty space' or 'available space', but the amount of space inside is the same either way). &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique rating #$&*OK ********************************************* Question: `q015. Explain how you have organized your knowledge of the principles illustrated by the exercises in this assignment. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): This exercise has been very heplful with alowing me gain knowlage on visulizing the cubic realionships with measure. Afer this assignment it has become mush easier for me to visualize how the block method can be utilized. ------------------------------------------------ Self-critique rating #$&* "