Jupiter is the largest planet in the solar system, with a diameter of approximately $9 x 10^{4}$ $9 x 10^4$ miles. Mercury is the smallest planet in the solar system, with a diameter of approximately $3 x 10^{3}$ $3 x 10^3$ miles. How many times larger is Jupiter than Mercury?

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Jupiter is the largest planet in the solar system, with a diameter of approximately $9 x 10^{4}$ $9 x 10^4$ miles. Mercury is the smallest planet in the solar system, with a diameter of approximately $3 x 10^{3}$ $3 x 10^3$ miles. How many times larger is Jupiter than Mercury?

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Answer 1 · 2016-11-29T12:58:58

Jupiter is $2.7 \times 10^{4}$ $2.7 xx 10^4$ times larger than Mercury

Explanation:

First we need to define 'times larger'. I will define this as the ratio of the approximate volumes of the planets.

Assuming both planets are perfect spheres:

Volume of Jupiter $(V_{j}) ≅ \frac{4}{3} π {(\frac{9}{2} \times 10^{4})}^{3}$ $(V_j) ~= 4/3 pi (9/2xx10^4)^3$

Volume of Mercury $(V_{m}) ≅ \frac{4}{3} π {(\frac{3}{2} \times 10^{3})}^{3}$ $(V_m) ~= 4/3 pi (3/2xx10^3)^3$

With the definition of 'times larger" above:

$\frac{V_{j}}{V_{m}} = \frac{\frac{4}{3} π {(\frac{9}{2} \times 10^{4})}^{3}}{\frac{4}{3} π {(\frac{3}{2} \times 10^{3})}^{3}}$ $V_j/V_m = (4/3 pi (9/2xx10^4)^3) / (4/3 pi (3/2xx10^3)^3)$

$= \frac{{(\frac{9}{2})}^{3} \times 10^{12}}{{(\frac{3}{2})}^{3} \times 10^{9}}$ $= ((9/2)^3xx10^12)/((3/2)^3xx10^9)$

$= \frac{9^{3}}{2^{3}} \cdot \frac{2^{3}}{3^{3}} \times 10^{3}$ $=9^3/2^3 * 2^3/3^3 xx 10^3$

$= \frac{3^{6}}{3^{3}} \times 10^{3}$ $=3^6/3^3 xx 10^3$

$= 3^{3} \times 10^{3}$ $=3^3 xx 10^3$

$= 27 \times 10^{3} = 2.7 \times 10^{4}$ $=27xx10^3 = 2.7xx10^4$

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Jupiter is the largest planet in the solar system, with a diameter of approximately $9 x 10^{4}$ $9 x 10^4$ miles. Mercury is the smallest planet in the solar system, with a diameter of approximately $3 x 10^{3}$ $3 x 10^3$ miles. How many times larger is Jupiter than Mercury?

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