A large sphere has a volume of 288*pi cubic units. A smaller sphere has a volume which is 64% of the volume of the larger sphere. What is the ratio of the radius of the smaller sphere to the radius of the larger sphere? Express your answer as a common fraction.
A large sphere has a volume of 288*pi cubic units. A smaller sphere has a volume which is 64% of the volume of the larger sphere. What is the ratio of the radius of the smaller sphere to the radius of the larger sphere? Express your answer as a common fraction.
V_s = 0.64*V_l = 0.64*288*pi
4pi*r^3 = 144*pi ==> r = 12
4pi*s^3 = 28*pi ==> s = 8
r/s = 8/12 = 2/3
Where did 144*pi come from???
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64% of 288 = 184.32
V = 4/3*pi*r3
288pi = 4/3*r3 184.32pi = 4/3*r3
288pi*3 / 4 = r3 184.32pi*3 / 4 = r3
r3 = 216 r3 = 3456/25
r = 6 r = 5.170643256
Ratio r : r = r = 5.170643256 / 6 ==> 0.861773876 ≈ 431/500
