Answer:
3.66 cm
Step-by-step explanation:
r = Radius of cylinder
h = Height of the cylinder = 11 cm
A = Total surface area of the cylinder = [tex]337\ \text{cm}^2[/tex]
Total surface area of a cylinder is given by
[tex]A=2\pi r^2+2\pi rh\\\Rightarrow A=2\pi r(r+h)\\\Rightarrow \dfrac{A}{2\pi}=r^2+rh\\\Rightarrow r^2+rh-\dfrac{A}{2\pi}=0\\\Rightarrow r^2+11r-\dfrac{337}{2\pi}=0\\\Rightarrow r^2+11r-53.64=0\\\Rightarrow 100r^2+1100r-5364=0\\\Rightarrow r=\dfrac{-1100\pm \sqrt{1100^2-4\times 100\left(-5364\right)}}{2\times 100}\\\Rightarrow r=3.66,-14.65[/tex]
So, the radius of the circular top is 3.66 cm.
