Answers to Planet Volumes
This answer sheet has
the answer to Planet Volume Questions:
Page with complete questions on Planet Volumes:
http://www.dailymathproblem.com/p/planetvolumesthispostusesdataon.html
Page with complete questions on Planet Volumes:
http://www.dailymathproblem.com/p/planetvolumesthispostusesdataon.html
What are
the volumes of the planets and the sun based on the assumption that all of the
planets and the sun are perfect spheres?
Sun and Planet Volumes


Radius km

Volume cubic km


Sun

695000

1.41E+18

Mercury

2440

6.08E+10

Venus

6052

9.29E+11

Earth

6378

1.09E+12

Mars

3397

1.64E+11

Jupiter

71492

1.53E+15

Saturn

60268

9.17E+14

Uranus

25559

6.99E+13

Neptune

24766

6.36E+13

Pluto

1150

6.37E+09

Calculation for earth
=(4/3) *3.14 *6.378^{3 }x 10^{9}
Note the (4/3) x 3.14 .6.378^{3} is 1086.8
1086.8 x 10^{9} is 1.087 x 10^{12}
In the problems below I round this to 1.09 x 10^{12 }
The volume is in cubic kilometers.
The volume is in cubic kilometers.
Calculate
the volume of each planet as a percent of the volume of Jupiter.
The volume of each planet was divided by the volume of Jupiter the largest planet.
Planet volumes as a percent of Jupiter


Radius km

Volume cubic km

Volume Planet over Volume Jupiter


Mercury

2440

6.08E+10

0.00%

Venus

6052

9.29E+11

0.06%

Earth

6378

1.09E+12

0.07%

Mars

3397

1.64E+11

0.01%

Saturn

60268

9.17E+14

59.91%

Uranus

25559

6.99E+13

4.57%

Neptune

24766

6.36E+13

4.16%

Pluto

1150

6.37E+09

0.00%

Calculation for Earth as a fraction of Jupiter:
1.09x 10^{12}
/ 1.53 x 10^{15}
(1.09)/1.53 = 7.1 x101
10^{12}/ 10^{15} is 10^{3}
Multiplying terms gets us
7.1 x 10^{4}
How many
planets might potentially fit inside an area of space the size of the volume of
Jupiter?
They
should all fit. Note the sum of each
planet as a fraction of Jupiter for the eight other planets is around 0.68 or
68%. Note that volume of Saturn is around 60 percent of Jupiter. The next highest volume planet, Neptune, is less than 5 percent of Jupiter.
How many
planets the size of Jupiter might fit inside an area the size of the sun?
Take the
ratio of the volume of the Sun to the volume of Jupiter
=1.41 x
10^{18}/ 1.53 x 10^{15}
This
comes out to around 921.
How many
planets the size of the earth might fit inside an area the size of the sun?
Take the
ratio of the volume of the Sun to the volume of the Earth.
1.41 x 10^{18}
/ 1.09 x 10^{12}
This
simplifies to 1.29 x 10^{6} or around 1,290,000 earths.^{}
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