Can someone please answer these for me? Converting!?

Question

1. A can is 40 cm long, 30 cm wide, and 45 m high. If the density of matter is 1g/cm³, what is the mass of water inside the can in kilogram?
2. Show how a speed of 40 kilometers per hr. can be converted to meter per second.
3. A supersonic aircraft has a speed of 2,200 milesper hour. Find each speed in meter per second.

Please explain answers.

Answer 1

1...40cm x 30cm x 45cm = 54,000cm³ @ 1g/cm³
= 54kg of water. (cm³ cancel out).

2...40kph = 40,000metres/hour ÷ 3,600seconds per hour = 11.11m/s (hours cancel out)

3...2,200 mph x 1.6km per mile = 3,520 kph
.....= 3,520,000 metres/hour ÷ 3,600 seconds/hour
.....= 977.8 m/s. (hours cancel out)

Answer 2

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Answer 3

1. Since you didn't say diameter, the can is 40x30x4500 cm3 (did you mean 45 cm?) which yields 540000 (5400) cm3=g and kilograms are 1000 grams so move 3 decimal places 540 (5.4) kg
2. 40 km/hr is 40000 m / 3600 seconds or 400/36 m/s or 100/9 or 11.111 m/s
3. 2200 mile / hr is 2200 * 1609.34 m/mile / 3600 sec = 22/36*1609.34 m/s = 893.488 m/s

Answer 4

1. You have to convert meters to centimeters to get a common measurement. So (1m = 100cm). From there you figure out the volume of the can. (LxWxH)

a. 40cm x 30cm x 4500cm = 5.4 x 10^6 cm^3

Now you need to figure out the mass of the water in the can. To do so use dimensional analysis as demonstrated below.

b. (1g/cm^3) x (5.4 x10^6 cm^3) = grams of water in the cup. (doing this will cancel out the cm^3 because the volume to mass would be as follows. (1g/1cm^3) x (1cm^3/1). From there just multiply the top and bottom numbers straight across from each other and you'll end up with (1g cm^3/cm^3) = 1g. as the cm^3's will cancel each other out since anything divided by itself equals 1.

So the final answer would be 5.4x10^6 grams of water.



2. Use dimensional analysis here to figure it out and convert it.

a. 40km/hr = x m/s

First lets convert the kilometers into meters.

40 km x 1000m/km = x meters. Since 1000m = 1km. This is simple multiplication as I used above: (40Km/1) * (1000m/Km) = 40,000mKm/Km so the end result is 40,000m since the kilometers on top and bottom of the equation cancel out to 1.

So we have 40,000 meters for the distance.

Now we figure out the hours into seconds.

1 hr = 60 minutes and 60 seconds = 1 minute.

1hr * 60 minutes/hr. * 60 seconds / minute = x seconds

multiplying across you get (1hr/1 * 60minute/1hr * 60 second/minute) = 3600(hr)(minute)(second)/(hr)*(minute)

The hr and minute end up cancelling so you get 3600 second.

Now we've got meters and seconds, so to find m/s we take (40000m/3600second) = x m/s

11.11 meters/second is the final answer.



3. This one you have to use a bit more dimensional analysis, though it's a bit more complex since you're converting from standard measurements to metric measurements.

a. Lets figure out the distance before we figure out the time.

1. (2200 miles * 5280 feet/mile) * 1 meter/3.281 feet) = x meters
2. (11,616,000 mile feet/mile) * (1meter/3.281 feet) = x meters
3. (11,616,000 mile feet meter/3.281 mile feet) = x meters
4. Since the miles and feet cancel out it becomes 3, 540,384 meters travelled so far.

b. Now lets figure out the time factor. From our previous equation we know that 1 hour = 3600 seconds. So to give the final answer we simply take the answer of distance and divide by time.

(3,540,384 meters/3600 seconds) = x meters/second

983.44 meters/ second is the final answer.

I hope this helps you out in the future.

For metric to standard conversions check out this link http://www.metric-conversions.org/

Answer 5

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