Sphere radius

We reduce the radius of the sphere by 1/3 of the original radius. How much percent does the volume and surface of the sphere change?

Correct answer:

p1 =  70.3704 %
p2 =  55.5556 %

Step-by-step explanation:

r1​=1 r2​=r1​−r1​/3=1−1/3=32​≐0.6667  V1​=34​⋅ π⋅ r13​=34​⋅ 3.1416⋅ 13≐4.1888 V2​=34​⋅ π⋅ r23​=34​⋅ 3.1416⋅ 0.66673≐1.2411  p1​=100⋅ V1​V1​−V2​​=100⋅ 4.18884.1888−1.2411​=271900​%=70.3704%
S1​=4π⋅ r12​=4⋅ 3.1416⋅ 12≐12.5664 S2​=4π⋅ r22​=4⋅ 3.1416⋅ 0.66672≐5.5851  p2​=100⋅ S1​S1​−S2​​=100⋅ 12.566412.5664−5.5851​=9500​%=55.5556%

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