Question

find the surface area of a cylinder with a height of 3 cm and a base diameter of 4 cm. 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 formula for radius \(r\) is \(r=\frac{d}{2}\), where \(d\) is the diameter. Given \(d = 4\) cm, so \(r=\frac{4}{2}=2\) cm.

Step2: Calculate the lateral surface area

The formula for the lateral surface area \(A_{l}\) of a cylinder is \(A_{l}=2\pi rh\). Substitute \(r = 2\) cm, \(h=3\) cm and \(\pi = 3.14\): \(A_{l}=2\times3.14\times2\times3=37.68\) \(cm^{2}\).

Step3: Calculate the area of the two bases

The formula for the area of a circle is \(A_{b}=\pi r^{2}\). The area of two bases \(A_{2b}=2\pi r^{2}\). Substitute \(r = 2\) cm and \(\pi = 3.14\): \(A_{2b}=2\times3.14\times2^{2}=2\times3.14\times4 = 25.12\) \(cm^{2}\).

Step4: Calculate the total surface area

The formula for the total surface area \(A\) of a cylinder is \(A=A_{l}+A_{2b}\). So \(A = 37.68+25.12=62.8\) \(cm^{2}\).

Answer:

\(62.8\) \(cm^{2}\)