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# spheres

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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.

Dec 5, 2020

#1
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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

Dec 5, 2020
#2
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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

Guest Dec 6, 2020