Question

find the surface area of a cylinder with a base diameter of 8 m and a height of 5 m. write your answer in terms of π, and be sure to include the correct unit.

Explanation:

Step1: Find the radius of the base

The diameter \( d = 8\space m \), so the radius \( r=\frac{d}{2}=\frac{8}{2} = 4\space m \).

Step2: Recall the formula for the surface area of a cylinder

The surface area of a cylinder \( S = 2\pi r^{2}+2\pi rh \), where \( r \) is the radius and \( h \) is the height.

Step3: Calculate the area of the two circular bases

The area of one circular base is \( \pi r^{2} \), so for two bases, it is \( 2\pi r^{2} \). Substituting \( r = 4 \), we get \( 2\pi(4)^{2}=2\pi\times16 = 32\pi \).

Step4: Calculate the lateral (curved) surface area

The lateral surface area is \( 2\pi rh \). Substituting \( r = 4 \) and \( h = 5 \), we get \( 2\pi\times4\times5=40\pi \).

Step5: Find the total surface area

Add the area of the two bases and the lateral surface area: \( S=32\pi + 40\pi=72\pi \). The unit is square meters (\( m^{2} \)).

Answer:

\( 72\pi \) square meters