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The mass of 1 cubic meter of a substance is 800 kg under

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The mass of 1 cubic meter of a substance is 800 kg under  [#permalink]

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New post Updated on: 01 Feb 2012, 14:47
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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)

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Originally posted by Michmax3 on 27 Sep 2010, 21:31.
Last edited by Bunuel on 01 Feb 2012, 14:47, edited 2 times in total.
Added the answer choices
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Re: Mass of a substance  [#permalink]

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New post 27 Sep 2010, 22:21
800kg --> 1 m3 = 1000000 cm3
1 g --> 1000000/(800*1000) cm3
= 1.25 cm
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Re: Mass of a substance  [#permalink]

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New post 28 Sep 2010, 00:18
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Michmax3 wrote:
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


800 kg - 1 cubic meter;
800,000 g - 1 cubic meter;
800,000 g - 1,000,000 cubic centimeters;
1 g - 1,000,000/800,000 = 10/8 = 1.25 cubic centimeters.

Answer: B.

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Re: Mass of a substance  [#permalink]

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New post 28 Sep 2010, 07:52
I got it quickly by just plugging in answer choices. Start with B then move to D if B is not correct and you will never need to plug in more than 2.
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Re: The mass of 1 cubic meter of a substance is 800 kg under  [#permalink]

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New post 25 Mar 2015, 02:56
8*10^5 =10^6
then 1= 10^6/ 8*10^5=1.25(B) This is easy way I think!!
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Re: The mass of 1 cubic meter of a substance is 800 kg under  [#permalink]

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New post 14 Oct 2018, 05:52
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Michmax3 wrote:
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

Answer: B

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Re: The mass of 1 cubic meter of a substance is 800 kg under  [#permalink]

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New post 14 Oct 2018, 07:03
Michmax3 wrote:
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.

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Re: The mass of 1 cubic meter of a substance is 800 kg under  [#permalink]

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New post 17 Oct 2018, 18:12
Michmax3 wrote:
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

Answer: B
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Re: The mass of 1 cubic meter of a substance is 800 kg under  [#permalink]

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New post 24 Oct 2018, 18:41
Michmax3 wrote:
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)


Answer:
1 m^3 =800 kg
10^6 cm^3 = 8* 10^5 gm
1 gm = 10/5 = 1.25
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Re: The mass of 1 cubic meter of a substance is 800 kg under  [#permalink]

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New post 24 Oct 2018, 23:59
Michmax3 wrote:
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

For more on units conversion, check: https://www.veritasprep.com/blog/2011/0 ... nd-ounces/
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Re: The mass of 1 cubic meter of a substance is 800 kg under &nbs [#permalink] 24 Oct 2018, 23:59
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