Radius of 2nd Sphere: Find Mass 5x Greater than 1st

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Homework Statement


Two spheres are cut from a certain uniform rock. One has a radius 4.50cm. The mass of the
other is 5 times greater. Find its radius


Homework Equations


r1 = 4.50cm
r2 = ? when mass is 5x greater


The Attempt at a Solution


Looking at this problem I first thought of somehow integrating the volume of a sphere
which is 4/3[tex]\pi[/tex]r3. But then i though i was just thinking too hard. it made more sense for the radius to be 5x the radius as i figure the mass was proportional to the radius.

so: r2 = 5(4.50cm) = 22.5cm

however i got this marked wrong as the answer was 7.69 cm. what wasn't I looking at clearly?
 
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afg_91320 said:

Homework Statement


Two spheres are cut from a certain uniform rock. One has a radius 4.50cm. The mass of the
other is 5 times greater. Find its radius


Homework Equations


r1 = 4.50cm
r2 = ? when mass is 5x greater


The Attempt at a Solution


Looking at this problem I first thought of somehow integrating the volume of a sphere
which is 4/3[tex]\pi[/tex]r3. But then i though i was just thinking too hard. it made more sense for the radius to be 5x the radius as i figure the mass was proportional to the radius.

so: r2 = 5(4.50cm) = 22.5cm

however i got this marked wrong as the answer was 7.69 cm. what wasn't I looking at clearly?

You started on the right track. Mass is proportional to volume, so the ratio 5 applies to the two radii how?
 
berkeman said:
You started on the right track. Mass is proportional to volume, so the ratio 5 applies to the two radii how?

well that would be proportional to the mass right? so if r2 is 5x in mass then r1 is 1/5(mass)? set up my equation to isolate r to get the radius...
 
afg_91320 said:
well that would be proportional to the mass right? so if r2 is 5x in mass then r1 is 1/5(mass)? set up my equation to isolate r to get the radius...

Mass is proportional to volume. Write the fraction V1/V2 out fully, and that will show you a ratio involving some form of the radii. That's where the 5x comes into play...