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V = 4/3 πr3 The formula for the volume of a sphere with r...
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v = 4/3 πr3

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

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adeb
Asked by adebrep:453
School not set Nigeria
11 January 2021

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judziy
Judziy answeredrep:1.9K
University of Benin Nigeria
11 January 2021
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v = 4/3 πr3 ------------- eqn(1)

Let rj and re be the radius of planet Jupiter and planet Earth respectively.

Let vj and ve 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,

rj = 11re

Re-writing eqn(1) in terms of ve, re and vj, rj,

ve = 4/3 πre3 ------------- eqn(2)

vj = 4/3 πrj3

Since  rj = 11re

vj = 4/3 π(11re)3

vj = 4/3 π(11)3re3

vj = (11)3(4/3 πre3)

from eqn(2), since ve = 4/3 πre3,

vj = (11)3ve

vj = 1331ve

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

Answer: C

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