The surface area of 2 spheres is a ratio of 64:729. What is the ratio of their radii?

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Answer 1 · 2017-12-12T12:26:22

8:27

The surface area of a sphere is given by #4pir^2#

Let r1 be the radius of the first sphere, and r2 be the radius of the second.

The problem statement gives us:

#(4pi*r1^2)/(4pi*r2^2) = 64/729#
...you can see that the #4pi# terms cancel.

therefore:
#(r1^2)/(r2^2) = 64/729#

Take the square root of everything you see:

#sqrt(r1^2)/sqrt(r2^2) = sqrt(64)/sqrt(729)# giving:

#(r1)/(r2) = 8/27#

GOOD LUCK