If the surface area of a sphere increased by 44%, find the percentage increase in diameter

Assessment: JAMB UTME - Mathematics - 1989 Subject: General Mathematics

Question 1 Report

If the surface area of a sphere increased by 44%, find the percentage increase in diameter
Answer Details
Surface Area of Sphere A = 4 π r 2
∴ A = 4 π ( D ) 2 2
=  ( D ) 2 2
=  π D2
When increased by 44% A =  144 π D 2 100
π ( 12 D ) 2 10  =  π ( 6 D ) 2 5
Increase in diameter =  6 D 5  - D =  1 5 D
Percentage increase =  1 5  x  1 100 %
= 20%

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