The ball

The ball has a radius of 2m. What percentage of the surface and volume is another sphere whose radius is 20% larger?

Correct answer:

p1 =  44 %
p2 =  72.8 %

Step-by-step explanation:

r1​=2 m r2​=(1+20/100)⋅ r1​=(1+20/100)⋅ 2=512​=2.4  S1​=4π⋅ r12​=4⋅ 3.1416⋅ 22≐50.2655 m2 S2​=4π⋅ r22​=4⋅ 3.1416⋅ 2.42≐72.3823 m2  p1​=100⋅ S1​S2​−S1​​=100⋅ 50.265572.3823−50.2655​=44=44%   Verifying Solution:  q=1.2 p11​=100⋅ (q2−1)=100⋅ (1.22−1)=44 % p1​ = p11​
V1​=34​⋅ π⋅ r13​=34​⋅ 3.1416⋅ 23≐33.5103 m3 V2​=34​⋅ π⋅ r23​=34​⋅ 3.1416⋅ 2.43≐57.9058 m3  p2​=100⋅ V1​V2​−V1​​=100⋅ 33.510357.9058−33.5103​=5364​=72.8=5364​%=72.8%   Verifying Solution:  p21​=100⋅ (q3−1)=100⋅ (1.23−1)=5364​=72.8 % p2​ = p21​

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