find the diameter of a cylinder when surface area and height is known

Question

a cylinder has a surface area of 1859cm and a height of 11.1cm. What is the diameter of the cylinder.

Answer 1

Surface area of cylinder (SA) = 2∏r(r+h)

Given h = 11.1cm

SA = 1859 cm^2

1859 = 2*3.14*r(r+11.1)

1859 = 6.28r(r+11.1)

Divide to each side by 6.28.

296.01 = r^2+11.1r

Subtract 296.01 from each side.

r^2+11.1r-296.01 = 0

Compare it to quadratic equation.

a = 1, b = 11.1, c = -296.01

r = [-b±√(b^2-4ac)]/2a

r = [-11.1±√(123.21+1184.04)]/2

r  = [-11.1±36.15]/2

r = [-11.1+36.15]/2 and r = [-11.1-36.15]/2

r = 25.05/2 and r = -47.25/2

r = 12.525 and r  = -23.625

Length is positive so radius is 12.525cm.

Diameter of cylinder(d) = 2r = 2*12.525 = 25.05cm.