Respuesta :
Radius = Diameter ÷ 2
Radius = 6 ÷ 2 = 3cm
Surface area = 2πr² + 2πrh
Surface area = 2 π (3)² + 2 π (3) (11.5) = 272.32 cm² (nearest hundredth)
Answer: 272.32 cm²
You're looking for the total surface of a cylinder, which is composed by two circles, and a rectangle conntecting them.
The area of the two circles is given by
[tex] A = \pi r^2 = \pi 3^2 = 9\pi[/tex]
The base of the rectangle is congruent to the circumference of the base circle, and the height is given. The circumference is given by
[tex] C = 2\pi r = 2\pi\cdot 3 = 6\pi [/tex]
So, the area of the rectangle is
[tex] 6\pi \cdot 11.5 = 69\pi [/tex]
The cylinder is consists of two circles and the rectangle, so its surface is
[tex] 69\pi +2\cdot 9\pi = 69\pi + 18\pi = 87\pi [/tex]
