Hitchhiking Through The Galaxy

Algebra Level 2

During one of my summer vacations, I was hitchhiking down Route 1. I happened to notice this globe just sitting out there. Upon further investigation, I learnt that the largest complete scale model of the solar system is in Aroostook County, Maine, U.S.A. The model extends along Route 1 with a 15 m model of the sun at one end and a 2.5 cm model of Pluto 64 km away. On this scale, what should the diameter of the model of Jupiter be, given that its actual diameter is 138350 km?

Note: For reference, Pluto's actual distance from the Sun is approximately 5.95 × 1 0 12 5.95 \times 10^{12} m, and the sun's actual diameter is approximately 1.39 × 1 0 9 1.39 \times 10^9 m.

Image Credit: Michael York
0.64 m 0.15 m 6.4 m 1.5 m

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Arron Kau by Arron Kau

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6 solutions

Lakshya Gupta
Mar 11, 2014

Be solving, we get that diameter of Jupiter is about 0.139 x 10^9m, which is 1/10th that of the sun, so in the model, the diameter of Jupiter will be 1/10th that of the Sun, that is 1.5m

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Yeah

Kahsay Merkeb - 7 years, 3 months ago

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correcto!

A Former Brilliant Member - 7 years, 3 months ago

0.139x10^8

Suresh Visweswara - 7 years, 3 months ago
Joe Lingle
Mar 18, 2014

138350 : 1390000 = x : 15 therefore x = 1.5

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Tasnim Rawat
Mar 21, 2014

convert the distance between sun and Pluto i.e 5.95 * 10 ^ 12 m = 64 km

so 5.95 * 10 ^ 12 m = 64000 m

1 m = 92968750 m

now radius of sun = 1.39 * 10 ^ 9 m = 15 m

15 m = 1.39 * 10 ^ 9 m

1 m = 92666666 m

By this diameter of Jupiter model can be 138350000/92968750 = 1.488 =1.5 m

138350000/92666666 = 1.49 = 1.5 m

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Mahendar Singh
Mar 20, 2014

15: (1.39 X 10 ^6) = x: (0.139 X 10^6)

Simple ratio

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Laxman Selvam
Mar 16, 2014

the jupiter's dia is 1/10th of the sun's. and hence even in the model the ration would be the same and hence the dia of jupiter's model would be 1.5m

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Hussain Syed
Mar 12, 2014

If you check, you will find that Jupiter's diameter is one-tenth that of sun. Applying the same scale, it is 1.5 m

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