find the diameter of a cylinder?

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 = 2∏r (r + h ) = 1859 cm

Height (h ) = 11.1 cm.

Diameter (d ) = ?

Substitute (h ) = 11.1 and  ∏ = 3.14 in 2∏r (r + h ) = 1859.

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

6.28r (r + 11.1) = 1859

6.28r ^2 + 6.28r (11.1) - 1859 = 0

6.28r ^2 + 69.708r - 1859 = 0, is quadratic, use the quadratic formula to find the roots of a related quadratic equation.

r  = [- b ± √(b ^2 - 4ac )]/2a.

Substitute b = 69.708, a = 6.28, and c = - 1859.

r = (- 69.708 ± √[(69.708^2) - 4 * 6.28 * (- 1859)])/2 * 6.28

  = (- 69.708 ± √[4859.2 + 46698.08])/12.56

  = (- 69.708 ± √51557.2)/12.56

 =  [- 69.708 ± 227.06]/12.56

r = [- 69.708 + 227.06]/12.56 (or) r = [- 69.708 - 227.06]/12.56

r  = 157.35/12.56 (or) r = - 296.76/12.56

r = 12.52 (or) r = - 23.62

Circle is base of cylinder.

Radius of circle (r ) = 12.52 cm.

Therefore, diameter of the cylinder (d ) = 2r

= 2 * 12.52

= 25.04.

Diameter (d ) = 25.04 cm.