unitsofvolume

course Phy 121

Question: `q001. There are 10 questions and 5 summary questions in this assignment.

How many cubic centimeters of fluid would require to fill a cubic container 10 cm on a side?

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Your solution:

The container’s volume is 10 cm x 10 cm x 10 cm which equals 1000 cm^3. That means it will take 1000 cm^3 to fill the container.

Confidence Assessment: 3

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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.

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Self-critique (if necessary): OK

Self-critique Rating: OK

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Question: `q002. How many cubes each 10 cm on a side would it take to build a solid cube one meter on a side?

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Your solution:

First we must find out how many cm are in 1 meter:

100 cm=1 meter

10 cm * (1 meter/ 100 cm)= 0.1 meter

Now, we find out how many 0.1 meter goes into 1 meter: 1/0.1= 10 cubes

The entire cube would take 10 x 10 x 10= 1000 cubes

Confidence Assessment: 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.

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Self-critique (if necessary): OK

Self-critique Rating: OK

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Question: `q003. How many square tiles each one meter on each side would it take to cover a square one km on the side?

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Your solution:

One km= 1000 meters

1 km * (1000m/ 1 km)= 1000 m

To find the volume we must solve for cubic meters:

1000 m x 1000 m x 1000 m= 1, 000, 000, 000 m^3 or 1000000000 cubes

Confidence Assessment: 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.

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Self-critique (if necessary):

I only needed to solve for square meters instead of cubic meters:

1000 m x 1000 m= 1, 000, 000 m^2

Self-critique Rating: 3

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Question: `q004. How many cubic centimeters are there in a liter?

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Your solution:

There are 1000 cm^3 in one liter.

Confidence Assessment: 3

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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.

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Self-critique (if necessary):

Note: a liter is the volume of a cube with 10 cm dimensions on each side.

Self-critique Rating: 3

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Question: `q005. How many liters are there in a cubic meter?

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Your solution:

There are 1000 cm^3 in one liter. Because there are 100 cm ^3 in 1 m^3, we find the # of liters by dividing 1000 by 100 cm^3:

1000/ 100 cm^3= 10 liters

Confidence Assessment: 1

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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.

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Self-critique (if necessary):

There are actually 1000 liters in a cm^3. This is because there are 10 of the 10 cm cubes in 1 m. There are also 10 layers giving us:

10 x 10 x 10= 1000 liters/ cm^3

Self-critique Rating: 3

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Question: `q006. How many cm^3 are there in a cubic meter?

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Your solution:

We’ve already solved for 1000 cm^3 in one liter. We also know that there are 1000 liters in 1 m^3. Therefore:

1000 cm^3* 1000 liters gives us 1000000 cm^3/ m^3.

Confidence Assessment: 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.

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Self-critique (if necessary): OK

Self-critique Rating: OK

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Question: `q007. If a liter of water has a mass of 1 kg then what is the mass of a cubic meter of water?

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Your solution:

Because there are 1000 liters in 1 m^3, we simply multiply 1 kg by 1000:

1 kg* 1000= 1000 kg

Confidence Assessment: 3

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Given Solution:

`aSince 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.

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Self-critique (if necessary): OK

Self-critique Rating: OK

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Question: `q008. What is the mass of a cubic km of water?

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Your solution:

The mass of a cubic km is 1000 times the mass of a cubic m.

As we previously solved, the mass of a cubic meter is 1000 kg.

1000 kg* 1000= 1,000,000 kg

Confidence Assessment: 2

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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.

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Self-critique (if necessary):

I first need to cube the 1000 m to find the equivalence in m^3.We then convert this to kg:

(1000 m)^3* 1000 kg/m^3= 1,000,000,000 kg

Self-critique Rating: 3

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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?

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Your solution:

First, 5 billion times 2 tells us that 10 billion liters of water is drunk a day. There are 1000 liters in one m^3. This means that there are 1,000,000 liters in one km^3.

(1 km^3)*(1,000,000 liters/ q km^3)*(1 day/ 10 billion liters)= 0.001 day

Confidence Assessment: 1

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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.

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Self-critique (if necessary):

I must remember that there are 10^9 m^3 per one cubic km. Knowing this, I can determine that there are 10^12 liters in one km^3.

(10^12 liters)/ (10^10 liters/day)= 100 days

Self-critique Rating: 3

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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?

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Your solution:

The surface area equation for a sphere is 4 pi r^2:

SA= 4 pi* 6400^2= 514457600 km^2

The volume is found using the equation:

V=A*h

V=510000000* 2 km= 1, 020, 000, 000 km^3

Confidence Assessment: 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.

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Self-critique (if necessary): OK

Self-critique Rating: OK

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Question: `q011. Summary Question 1: How can we visualize the number of cubic centimeters in a liter?

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Your solution:

We can visualize that it takes 10 cm cubes in rows of 10. We need 10 sets of these rows. Therefore 10 x 10 x 10 gives us 1000 cm^3.

Confidence Assessment: 3

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Given Solution:

`aSince 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.

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Self-critique (if necessary): OK

Self-critique Rating: OK

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Question: `q012. Summary Question 2: How can we visualize the number of liters in a cubic meter?

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Your solution:

Because there are 1000 cm in 1 m and there are 1000 cm in 1 liter, we can use these two facts to find that there are 1000 liters in 1 m^3.

Confidence Assessment: 3

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Given Solution:

`aSince 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.

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Self-critique (if necessary): OK

Self-critique Rating: OK

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Question: `q013. Summary Question 3: How can we calculate the number of cubic centimeters in a cubic meter?

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Your solution:

We know that one meter is made up of 1000 cm. Therefore if we multiply 100 cm x 100 cm x 100 cm, we can solve for the number of cubic cm in one cubic m:

100 cm x 100 cm x 100 cm= 1,000,000 cm^3

Confidence Assessment: 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.

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Self-critique (if necessary): OK

Self-critique Rating: OK

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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?

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Your solution:

There are not. We must cube the 1000 meters/ kilometer to find the number of cubic meters/cubic kilometers:

1000 m* 1000 m* 1000 m= 1,000,000,000 m^3

1 km* 1 km* 1 km= 1 km^3 which equals 1 billion m^3

Confidence Assessment: 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.

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Self-critique (if necessary): OK

Self-critique Rating: OK

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Question: `q015. Explain how you have organized your knowledge of the principles illustrated by the exercises in this assignment.

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Self-critique (if necessary):

I have organized my knowledge by keeping record of the unit conversions for each unit of volume.

Self-critique Rating: 3

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