what is the surface area of the cylinder? use π ≈ 3.14 and write your answer as a decimal rounded to the…

Explanation:

Step1: Find the radius

The diameter $d = 16$ in, so the radius $r=\frac{d}{2}=\frac{16}{2}=8$ in.

Step2: Calculate the area of the two - bases

The area of a circle is $A_{base}=\pi r^{2}$. The area of two bases $A_{2 - bases}=2\pi r^{2}$. Substitute $r = 8$ in and $\pi\approx3.14$, we get $A_{2 - bases}=2\times3.14\times8^{2}=2\times3.14\times64 = 401.92$ square inches.

Step3: Calculate the lateral - surface area

The formula for the lateral - surface area of a cylinder is $A_{lateral}=2\pi r h$. Substitute $r = 8$ in, $h = 7$ in and $\pi\approx3.14$, we get $A_{lateral}=2\times3.14\times8\times7=351.68$ square inches.

Step4: Calculate the total surface area

The total surface area of a cylinder $A = A_{2 - bases}+A_{lateral}$. So $A=401.92 + 351.68=753.6$ square inches.

Answer:

$753.6$