Asked by Peter

Two spheres are used in a certain machine. One has a volume of 7 cm3 and the other has a volume of 189 cm3. The radius of the small sphere is what fraction of the radius of the large sphere? Which of the following represents the first step to solve this problem?

Question options:

189 ÷ 7
73
189√3
189 ÷ 3

I think option 4 but it says that I'm incorrect. Please help.
Answered by Reiny
the volumes of the two spheres would be proportional to the cube of their radii.
so
r1^3 / r2^3 = 7 / 189 , where r1 is smaller and r2 is the larger radius
(r1/r2)^3 = 7/189 = 1/27
r1 / r2 = 1/3

the radius of the smaller is 1/3 of the radius of the larger.
None of the given choices are correct.



Answered by Peter
What did you do first?
Answered by Reiny
Did you not look at my solution?

you could do it the long way .....


(4/3)π r1^3 = 189
r2^3 = 189(3/4)(1/π) = 567/4π
r2 = (567/4π)^(1/3) = 3.56006...

similarly
(4/3)π r2^3 = 7
r1 = ...
= 1.186687...

r2/r1 = 3.560063... / 1.186687.. = 3/1
so the smaller radius is 1/3 the larger
Answered by Peter
Ok, thank you :). Sorry for the trouble.
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