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# The mass of 1 cubic meter of a substance is 800 kilograms under certai

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Re: The mass of 1 cubic meter of a substance is 800 kilograms under certai [#permalink]
Yalephd
Thanks, Bunuel. Sorry about posting in the wrong forum.
I am confused, because isn't 1,000,000 cubic centimeters / 800,000 g the density of the substance. That is 1.25 cubic cubic centimeters per gram of the substance. The question asked for volume, not density.

Density is mass divided by volume. So density of the given substance will be mass/volume=800kg/1m^3=800 kg/m^3 or 1g/1.25cm^3=0.8 g/cm^3.

Next, ask yourself if 800,000 g is equivalent to 1,000,000 cubic centimeters then 1 g is equivalent to how many cubic centimeters? --> 1 g - 1,000,000/800,000 = 10/8 = 1.25 cubic centimeters.

Hope it's clear.
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Re: The mass of 1 cubic meter of a substance is 800 kilograms under certai [#permalink]
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Michmax3
The mass of 1 cubic meter of a substance is 800 kg under certain conditions. What is the volume in cubic centimeters of 1 gram of this substance under these conditions? (1 kg =1,000 grams and 1 cubic meter = 1,000,000 cubic centimeters)

A. 0.8
B. 1.25
C. 8.0
D. 12.50
E. 80

GIVEN: 1 cubic METER of the substance weighs 800 KILOGRAMS
1 kg =1,000 grams, so we can write: 1 cubic METER of the substance weighs 800,000 GRAMS
1 cubic meter = 1,000,000, so we can write: 1,000,000 cubic CENTIMETERS of the substance weighs 800,000 GRAMS

What is the volume in cubic centimeters of 1 gram of this substance under these conditions?
Take last line and divide both values by 800,000 to get: 1,000,000/800,000 cubic CENTIMETERS of the substance weighs 800,000/800,000 GRAMS
Simplify to get: 1.25 cubic CENTIMETERS of the substance weighs 1 GRAM

Cheers,
Brent
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Re: The mass of 1 cubic meter of a substance is 800 kilograms under certai [#permalink]
Michmax3
The mass of 1 cubic meter of a substance is 800 kg under certain conditions. What is the volume in cubic centimeters of 1 gram of this substance under these conditions? (1 kg =1,000 grams and 1 cubic meter = 1,000,000 cubic centimeters)

A. 0.8
B. 1.25
C. 8.0
D. 12.50
E. 80
$$1\,{{\rm{m}}^3}\,\, \leftrightarrow \,\,800\,{\rm{kg}}\,\,\,\,\,\,\,\left( {1\,{\rm{kg}}\,\, = \,\,{{10}^3}\,{\rm{g}}\,\,\,\,\,{\rm{;}}\,\,\,\,1\,{{\rm{m}}^3}\,\, = \,\,{{10}^6}\,{\rm{c}}{{\rm{m}}^3}} \right)$$
$${\rm{1}}\,\,{\rm{g}}\,\,\, \leftrightarrow \,\,{\rm{?}}\,\,{\rm{c}}{{\rm{m}}^3}$$

PERFECT opportunity for the UNITS CONTROL, one of the most powerful tools in our method!

$$?\,\,\, = \,\,\,1\,\,{\rm{g}}\,\,\,\left( {{{1\,{\rm{kg}}\,} \over {{{10}^3}\,{\rm{g}}}}\matrix{\\ \nearrow \cr \\ \nearrow \cr \\ \\ } } \right)\,\,\,\,\left( {{{1\,{{\rm{m}}^3}\,} \over {800\,{\rm{kg}}}}\matrix{\\ \nearrow \cr \\ \nearrow \cr \\ \\ } } \right)\,\,\,\,\left( {{{{{10}^6}\,{\rm{c}}{{\rm{m}}^3}\,} \over {1\,{{\rm{m}}^3}}}\matrix{\\ \nearrow \cr \\ \nearrow \cr \\ \\ } } \right)\,\,\,\,\,\, = \,\,\,\,{{{{10}^6}} \over {{{10}^3} \cdot 800}} = {{10} \over 8} = 1{1 \over 4}\,\,\,\,\,\,\,\,\left[ {{\rm{c}}{{\rm{m}}^3}} \right]$$

Obs.: arrows indicate licit converters.

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Re: The mass of 1 cubic meter of a substance is 800 kilograms under certai [#permalink]
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Michmax3
The mass of 1 cubic meter of a substance is 800 kg under certain conditions. What is the volume in cubic centimeters of 1 gram of this substance under these conditions? (1 kg =1,000 grams and 1 cubic meter = 1,000,000 cubic centimeters)

A. 0.8
B. 1.25
C. 8.0
D. 12.50
E. 80

Since 800 kg = 800 x 1000 = 800,000 grams and 1 m^3 = 1,000,000 cm^3, we can create the ratio, where x is the number of cubic centimeters of 1 gram of the substance:

800,000/1,000,000 = 1/x

8/10 = 1/x

8x = 10

x = 1.25

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The mass of 1 cubic meter of a substance is 800 kilograms under certai [#permalink]
Michmax3
The mass of 1 cubic meter of a substance is 800 kg under certain conditions. What is the volume in cubic centimeters of 1 gram of this substance under these conditions? (1 kg =1,000 grams and 1 cubic meter = 1,000,000 cubic centimeters)

A. 0.8
B. 1.25
C. 8.0
D. 12.50
E. 80

Is there an easy way to do these types of problems? I spent a lot of time trying to figure out the correct conversions and then still got the wrong answer (correct digits, just was off by a power of 10)

Just replace the given units with the required units as per the relation.

Weight 800 kg => Volume 1 m^3

Weight 800 * 1000 grams => Volume 1 *100 cm *100 cm * 100 cm

Weight 1 gram => Volume 1000000 cm^3 /800 * 1000

Weight 1 gram => Volume 5/4 = 1.25 cm^3

Originally posted by KarishmaB on 25 Oct 2018, 00:59.
Last edited by KarishmaB on 17 Oct 2022, 03:46, edited 1 time in total.
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Re: The mass of 1 cubic meter of a substance is 800 kilograms under certai [#permalink]
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Re: The mass of 1 cubic meter of a substance is 800 kilograms under certai [#permalink]
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