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

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.

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

Answer: B

Cheers,
Brent

\(1\,{{\rm{m}}^3}\,\, \leftrightarrow \,\,800\,{\rm{kg}}\,\,\,\,\,\,\,\left( {1\,{\rm{kg}}\,\, = \,\,{{10}^3}\,{\rm{g}}\,\,\,\,\,{\rm{;}}\,\,\,\,1\,{{\rm{m}}^3}\,\, = \,\,{{10}^6}\,{\rm{c}}{{\rm{m}}^3}} \right)\)
\({\rm{1}}\,\,{\rm{g}}\,\,\, \leftrightarrow \,\,{\rm{?}}\,\,{\rm{c}}{{\rm{m}}^3}\)

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.

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

Answer: B

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

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