Question

find the surface area of this cylinder
use 3.14 for π.
5 cm
6 cm
sa = ? cm²

Explanation:

Step1: Find the radius

The diameter \(d = 5\) cm, so the radius \(r=\frac{d}{2}=\frac{5}{2}=2.5\) cm.

Step2: Calculate the area of the two circular bases

The formula for the area of a circle is \(A=\pi r^{2}\). For two bases, \(A_{bases}=2\pi r^{2}\). Substitute \(r = 2.5\) cm and \(\pi=3.14\):
\(A_{bases}=2\times3.14\times(2.5)^{2}=2\times3.14\times6.25 = 39.25\) \(cm^{2}\)

Step3: Calculate the lateral surface area

The formula for the lateral surface area of a cylinder is \(A_{lateral}=2\pi rh\). Here \(h = 6\) cm, \(r = 2.5\) cm, \(\pi=3.14\).
\(A_{lateral}=2\times3.14\times2.5\times6=3.14\times30 = 94.2\) \(cm^{2}\)

Step4: Calculate the total surface area

\(SA=A_{bases}+A_{lateral}\)
\(SA=39.25 + 94.2=133.45\) \(cm^{2}\)

Answer:

\(133.45\) \(cm^{2}\)