Question

find the surface area of a cylinder with a base diameter of 10 m and a height of 9 m. 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 \(d = 10m\), so the radius \(r=\frac{d}{2}=\frac{10}{2}=5m\)

Step2: Calculate the area of the two bases

The formula for the area of a circle is \(A_{base}=\pi r^{2}\). For two bases, \(A_{two - bases}=2\pi r^{2}\). Substitute \(r = 5m\) and \(\pi=3.14\), we get \(A_{two - bases}=2\times3.14\times5^{2}=2\times3.14\times25 = 157m^{2}\)

Step3: Calculate the lateral surface area

The formula for the lateral surface area of a cylinder is \(A_{lateral}=2\pi r h\). Substitute \(r = 5m\), \(h = 9m\) and \(\pi=3.14\), we get \(A_{lateral}=2\times3.14\times5\times9=282.6m^{2}\)

Step4: Calculate the total surface area

The formula for the surface area of a cylinder is \(A = A_{two - bases}+A_{lateral}\). So \(A=157 + 282.6=439.6m^{2}\)

Answer:

\(439.6m^{2}\)