A right circular cone has a base radius of \(4\) and a height of \(6.\) A right circular cylinder also has a base radius of \(4\) and a height of \(6.\) Let \(A\) be the lateral surface area of the cone, and let \(B\) be the lateral surface area of the cylinder. Find \(A/B.\)
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+23246 Formula for the lateral surface area of a cone: A = pi · r · sqrt( h2 + r2 )
A = pi · 4 · sqrt( 62 + 42 )
A = pi · 4 · sqrt( 52 )
A = 8 · pi · sqrt(13)
Formula for the lateral surface area of a cylinder: A = 2 ·pi · r · h
A = 2 ·pi · 4· 6
A = 48 ·pi
Comparing the two: 8 · pi · sqrt(13) / 48 ·pi = sqrt(13) / 6
