The curved surface area of a cylinder of radius xcm and length 3x+2cm is 32pi cm^2. Form an equation, in terms of x, and solve it to find the length of the cylinder

Answer 1

Surface area of cylinder = 2 * area of circular bases + circumference of circular base * height

The portion of the surface area that is given is highlighted in bold above as 32* pi.

(pi * 2x )(3x+2) = 32

pi * (3x^2 + 2x) = 16 <--- divides both sides by 2 and distributes the x that remains

(pi*3) x^2 + (2 * pi) x - 16 = 0

A = (pi * 3) B = 2*pi C = -16

x = [-2*pi +or- sqrt ( 4 * pi^2 - 4 * pi * 3 * -16) ] / (2 * pi * 3)

= [ -2 *pi +or- sqrt( 4 * pi^2 + 192*pi)]/(6*pi)

= [ -2 * pi +or- 2 * sqrt( 2 * pi^2 + 96*pi)]/(6 * pi)

=[ -pi +or- sqrt(2 * pi^2 + 96*pi)]/(3 * pi)

negative branch results in negative measures

x =[ -pi + sqrt( 2 * pi^2 + 96*pi)]/(3*pi)

which is APPROXIMATELY 1.586466021153355674307990859508.....