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 4and a height of 6. Let A be the lateral surface area of the cone, and let B

Question

be the lateral surface area of the cylinder. Find A/B.

Answer 1

surface area of cone: pi * r * ( r + sqrt( r^2 + h^2))

surface area of cylinder: 2*pi*r*h + 2*pi * r^2

A = pi * 4 * ( 4 + sqrt(4^2 + 6^2)) = pi * 4 * ( 4 + sqrt(16+36)) = pi *4 * ( 4 + sqrt(52)) =

pi * 4 * ( 4 + 2 * sqrt(13))

B = 2*pi*4*6 + 2 * pi * 4^2 = 48*pi + 32 * pi = 80*pi

A/B = pi * 4 * (4 + 2 * sqrt(13)) / 80 * pi

= ( 4 + 2 * sqrt(13))/ 20

= ( 2 + sqrt(13)) / 10