find the surface area of the cylinder.\nthe surface area of the given cylinder is (square) in². (simplify…

find the surface area of the cylinder.\nthe surface area of the given cylinder is (square) in². (simplify your answer. type an exact answer in terms of (pi). use integers or decimals for any numbers in the expression.)

find the surface area of the cylinder.\nthe surface area of the given cylinder is (square) in². (simplify your answer. type an exact answer in terms of (pi). use integers or decimals for any numbers in the expression.)

Answer

Explanation:

Step1: Calculate area of two bases

The area of a circle is $A_{base}=\pi r^{2}$. Given $r = 11$ in, the area of two bases is $A_{2 - bases}=2\pi r^{2}=2\pi\times(11)^{2}=242\pi$ in².

Step2: Calculate lateral - surface area

The formula for the lateral - surface area of a cylinder is $A_{lateral}=2\pi r h$. Here, $r = 11$ in and $h = 16$ in, so $A_{lateral}=2\pi\times11\times16 = 352\pi$ in².

Step3: Calculate total surface area

The total surface area of a cylinder $A=A_{2 - bases}+A_{lateral}$. Substitute the values: $A = 242\pi+352\pi=594\pi$ in².

Answer:

$594\pi$