Question

find the surface area of a cylinder with a height of 9 in and a base diameter of 4 in. use the value 3.14 for π, and do not do any rounding. be sure to include the correct unit.

Explanation:

Step1: Calculate the radius

The diameter $d = 4$ in, so the radius $r=\frac{d}{2}=\frac{4}{2}=2$ in.

Step2: Calculate the area of the two bases

The area of a circle is $A_{base}=\pi r^{2}$. For two bases, $A_{bases}=2\pi r^{2}$. Substituting $r = 2$ in and $\pi=3.14$, we get $A_{bases}=2\times3.14\times2^{2}=2\times3.14\times4 = 25.12$ in$^{2}$.

Step3: Calculate the lateral - surface area

The lateral - surface area of a cylinder is $A_{lateral}=2\pi r h$. Substituting $r = 2$ in, $h = 9$ in and $\pi = 3.14$, we have $A_{lateral}=2\times3.14\times2\times9=113.04$ in$^{2}$.

Step4: Calculate the total surface area

The total surface area $A = A_{bases}+A_{lateral}$. So $A=25.12 + 113.04=138.16$ in$^{2}$.

Answer:

$138.16$ in$^{2}$