course phy 121 6/20 7 pm 004. Units of volume measure*********************************************
.............................................
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): OK ------------------------------------------------ Self-critique rating #$&* ********************************************* Question: `q002. How many cubes each 10 cm on a side would it take to build a solid cube one meter on a side? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: It would take ten cubes to build a solid cube one meter on a side. One meter = 100 cm. So, 100 / 10 = 10. So, ten cubes at 10 cm each would build a row that was 1 meter. So, you would need 10 layers with 10 rows of 10 cubes so, 10 * 10 * 10 would be 1000 small cubes. confidence rating #$&* 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
.............................................
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): I understand the concept but may need a bit more of an explanation. ??????????????? Why did you include 10 layers and 10 rows? I understand why you would need 10 rows of 10 cubes each but what is the difference between the layers and the rows???????????? ------------------------------------------------ Self-critique rating #$&*3 ********************************************* Question: `q003. How many square tiles each one meter on each side would it take to cover a square one km on the side? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: It would take 1000 ^ 2 m squares to cover the one km square. It is squared because you need 1000 rows of 1000 tiles. So, 1,000,000 squares. confidence rating #$&* 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
.............................................
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): I should have said it takes 1000 meters to make a km. And I should have said that 1 km on a side would take 1000 rows each with 1000 such times to cover 1 square km. ------------------------------------------------ Self-critique rating #$&*3 ********************************************* Question: `q004. How many cubic centimeters are there in a liter? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: confidence rating #$&* 0 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
.............................................
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): I really did not know where to start this question. I didn’t know or at least forgot that a liter is the volume of a cube 10 cm on a side. If I knew this, I would have been able to figure out the rest of the problem by determining the volume by 10 cm * 10 cm * 10 cm = 1000 cm^3 and then come to the conclusion that there are 1000 cubic centimeters in a liter. ------------------------------------------------ Self-critique rating #$&* 3 ********************************************* Question: `q005. How many liters are there in a cubic meter? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: A liter is the volume of a cube 10 cm on a side, so it would take ten layers of ten rows made of ten cubes to make a cubic meter. So, 10 * 10 * 10 = 1000 liters in a cubic meter. confidence rating #$&* 2 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
.............................................
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):OK ------------------------------------------------ Self-critique rating #$&* ********************************************* Question: `q006. How many cm^3 are there in a cubic meter? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: There are 100 cm in a meter. So 1 m^3 = (100cm)^3 = 1,000,000 cm^3 in a m^3. confidence rating #$&* 2 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
.............................................
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): OK ------------------------------------------------ Self-critique rating #$&* ********************************************* Question: `q007. If a liter of water has a mass of 1 kg the what is the mass of a cubic meter of water? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: There are 1000 liters in a cubic meter and so if the mass of one liter is 1 kg, then the mass of one m^3 would have to be 1000 times that of the liter so it would be 1000 kg. confidence rating #$&* 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
.............................................
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 didn’t explain the procedure as well as I should have. ------------------------------------------------ Self-critique rating #$&*3 ********************************************* Question: `q008. What is the mass of a cubic km of water? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: The mass of a cubic meter is 1000 kg. Therefore the mass of a cubic km would have to be 1000 times that of a cubic meter so it would be 1,000,000 kg. confidence rating #$&* 2 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
.............................................
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. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ??????????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.???????????
.............................................
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): I needed to explain the process more and probably use proper scientific notation and stay consistent throughout my problem. ------------------------------------------------ Self-critique rating #$&* ********************************************* Question: `q010. The radius of the Earth is approximately 6400 kilometers. What is the surface area of the Earth? If the surface of the Earth was covered to a depth of 2 km with water that what would be the approximate volume of all this water? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: The surface area of a sphere is 4 pi r^2. So, 4 pi (6400 km)^2 = 163,840,000 pi km^2. Volume = area * altitude so V= 163,840,000 pi km^2 * 2 km = 327,680,000 pi km^3. The approximate volume of all this water would be 1,029,439,488 km^3. confidence rating #$&* 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
.............................................
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): I didn’t make note that the 2 km would change the diameter which would change the surface area. ????????????I also did not round my final number to a nice number..should I have?????????
.............................................
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): I needed to say that a liter is a cube 10 cm on a side. ------------------------------------------------ Self-critique rating #$&*3 ********************************************* Question: `q012. Summary Question 2: How can we visualize the number of liters in a cubic meter? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: The number of liters in a cubic meter is easily visualized by thinking of 10 cubes measuring one meter. Then we visualize 10 layers with 10 rows made of 10 cubes each. That makes 1000 ten cm cubes. Each ten cm cube is a liter so it would be 1000 liters in a cubic meter. confidence rating #$&* 2 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
.............................................
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): I should have explained each step a little more clearly. I didn’t explain that a liter is a cube 10 cm on a side. ------------------------------------------------ Self-critique rating #$&*3 ********************************************* Question: `q013. Summary Question 3: How can we calculate the number of cubic centimeters in a cubic meter? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: 1 m^3 = (100cm)^3 = 1,000,000 cm^3. confidence rating #$&* 2 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
.............................................
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): I did not show both ways. ------------------------------------------------ Self-critique rating #$&*3 ********************************************* Question: `q014. Summary Question 4: There are 1000 meters in a kilometer. So why aren't there 1000 cubic meters in a cubic kilometer? Or are there? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: There are not. The reason is because it has to be cubed. confidence rating #$&* 1 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
.............................................
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): I fell victim to the typical answer. I did not explain that kilometers and cubic kilometers don’t measure the same sort of thing. Kilometers measure distance and cubic kilometers measure volume.