Question

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find the surface area of a cylinder with a base diameter of 12 in and a height of 9 in. use the value 3.14 for π, and do not do any rounding. be sure to include the correct unit.

Explanation:

Step1: Find the radius

The radius \(r\) is half of the diameter. Given diameter \(d = 12\) in, so \(r=\frac{d}{2}=\frac{12}{2}=6\) in.

Step2: Calculate the area of the two bases

The area of a circle is \(A_{base}=\pi r^{2}\). For two bases, \(A_{two - bases}=2\pi r^{2}\). Substitute \(r = 6\) in and \(\pi=3.14\), we get \(A_{two - bases}=2\times3.14\times6^{2}=2\times3.14\times36 = 226.08\) in².

Step3: Calculate the lateral surface area

The formula for the lateral surface area of a cylinder is \(A_{lateral}=2\pi r h\). Substitute \(r = 6\) in, \(h = 9\) in and \(\pi=3.14\), we have \(A_{lateral}=2\times3.14\times6\times9=339.12\) in².

Step4: Calculate the total surface area

The total surface area \(A = A_{two - bases}+A_{lateral}\). So \(A=226.08 + 339.12=565.2\) in².

Answer:

\(565.2\) square inches