A heavy rainstorm dumps 1.0 cm of rain on a city 5 km wide and 8 km long in a 2-h period. How many metric tons (1 metric ton = 10^3 kg) of water fell on the city? [1 cm^3 of water has a mass of 1 gram = 10^-3 kg.]
Thats the actual question straight from the book. I have no ssense of direction on what to do. I know i have to convert some units of measurement but i have no clue?
2007-09-12 02:41:29 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Physics
5km = 5000m
8km = 8000m
1cm = 0.01m
Area (or Volume) = 5000 * 8000 * 0.01 = 400,000 m^3 of water.
1 m^3 of water weighs 1000kg.
Therefore, 400,000 m^3 water has a mass of-:
400,000 * 1000 = 4 * 10^8 kg. or 400 million kilograms.
In metric tons-:
4 * 10^8 / 1000 = 400,000 metric tons.
2007-09-12 02:56:13 · answer #1 · answered by Doctor Q 6 · 0⤊ 0⤋
This one is quite simple. It goes like this:
The area of the city is 5 * 8 km^2
= 40 sq. km
Since 1 km = 1000 m
= 1000 * 100 cm
= 1 * 10^5 cm
40 sq. km = 40 * (1 * 10^5)^2
= 40 * 10^10 sq. cm
Now, since the height of rain is just 1 cm, volume of water is also 40 * 10^10 cu. cm.
Since, 1 cu cm water = 1 gm
40 * 10^10 cu cm = 40 * 10^10 gm
1 metric ton = 10^3 kg
= 10^3 * 10^3 g
= 10^6 g
Therefore,
40*10^10 gm = 40*10^10/10^6 = 4*10^5 metric tonne
Hope this helped...
2007-09-12 09:59:19 · answer #2 · answered by {flick} 3 · 0⤊ 0⤋
First you can calculate the volume of the rain water by using the 8 km, 5 km and 1.0 cm.
Covert all the length to cm which gives you 8x10^5, 5x10^5 and 1.0. Now to get the volume just mulitiply them and you get 4x10^11 cm^3
Now use that 1 cm^3 has the mass of 1 gram. This gives you that the rain water's total mass is 4x10^11 gram. Then covert it to kg to get 4x10^8 kg.
Then use the1 metric ton is 10^3 kg to get that rain water's mass in metric ton is 4x10^5 metric ton.
2007-09-12 10:03:01 · answer #3 · answered by snowboll_2000 1 · 0⤊ 0⤋
Volume = 0.01m*5*10^3*8*10^3= 40*10^4 m^3
1m^3 = 10^6cm^3 has a mass of 1metric ton
so The mass is 4*10^5= 40,000 metric tons
I don´t see the need of time
2007-09-12 09:55:36 · answer #4 · answered by santmann2002 7 · 0⤊ 1⤋
5 km= 500 000cm
8 km= 800 000cm
Area of the city = 500 000cm x 800 000cm
= 400 000 000 000cm^2
Volume = 1.0 cm x 400 000 000 000cm
= 400 000 000 000cm^3
= 400 000 000 000g
= 400 000 000 kg
= 4x 10^ 8 kg
= 4 x (10^8 / 10^3)mt
= 4 x 10^5 mt
2007-09-12 10:03:27 · answer #5 · answered by fine 2 · 1⤊ 0⤋