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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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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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