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​

Try another example


Did you find an error or inaccuracy? Feel free to write us. Thank you!







Tips for related online calculators
Our percentage calculator will help you quickly and easily solve a variety of common percentage-related problems.
Tip: Our volume units converter will help you convert volume units.

You need to know the following knowledge to solve this word math problem:

Units of physical quantities:

Grade of the word problem:


 
We encourage you to watch this tutorial video on this math problem: video1

Related math problems and questions: