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v = 4/3 πr^{3}

The formula for the volume of a sphere with radius r is shown above. The radius of the planet Jupiter is about 11 times the radius of planet Earth. Assuming that planets are spheres, about how many times larger is the volume of Jupiter than the volume of Earth?

A) 11

B) 121

C) 1,331

D) 1,775

**Comments**

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v = 4/3 πr^{3} ------------- eqn(1)

Let r_{j} and r_{e} be the radius of planet Jupiter and planet Earth respectively.

Let v_{j} and v_{e} be the volume of planet Jupiter and planet Earth respectively.

If the radius of the planet Jupiter is about 11 times the radius of planet Earth,

r_{j} = 11r_{e}

Re-writing eqn(1) in terms of v_{e}, r_{e} and v_{j}, r_{j},

v_{e} = 4/3 πr_{e}^{3} ------------- eqn(2)

v_{j} = 4/3 πr_{j}^{3}

Since r_{j} = 11r_{e}

v_{j} = 4/3 π(11r_{e})^{3}

v_{j} = 4/3 π(11)^{3}r_{e}^{3}

v_{j} = (11)^{3}(4/3 πr_{e}^{3})

from eqn(2), since v_{e} = 4/3 πr_{e}^{3},

v_{j} = (11)^{3}v_{e}

v_{j} = 1331v_{e}

Thus, the volume of Jupiter is 1331 times larger than that of Earth's

**Answer: C**

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