Question

find the surface area of a cylinder with a base diameter of 8 in and a height of 6 in.

write your answer in terms of \\(\pi\\), and be sure to include the correct unit.

Explanation:

Find the radius of the cylinder base

The base diameter is \(d = 8\text{ in}\).
The radius \(r\) is half of the diameter:

$$r = \frac{d}{2} = \frac{8}{2} = 4\text{ in}$$

Calculate the area of the two circular bases

Using the Circle Area concept:
The area of one circular base is:

$$A_{\text{base}} = \pi r^2 = \pi (4)^2 = 16\pi\text{ in}^2$$

Since a cylinder has two bases, their combined area is:

$$2 \cdot A_{\text{base}} = 2 \cdot 16\pi = 32\pi\text{ in}^2$$

Calculate the lateral surface area

Using the Circle Circumference concept:
The lateral area is the circumference of the base multiplied by the height \(h = 6\text{ in}\):

$$A_{\text{lateral}} = 2\pi r h = 2\pi (4)(6) = 48\pi\text{ in}^2$$

Calculate the total surface area

The total surface area \(S\) is the sum of the base areas and the lateral area:

$$S = 2 A_{\text{base}} + A_{\text{lateral}} = 32\pi + 48\pi = 80\pi\text{ in}^2$$

Answer:

Find the surface area of a cylinder with a base diameter of 8 in and a height of 6 in.

Write your answer in terms of \(\pi\), and be sure to include the correct unit.

<blank>\(80\pi\text{ in}^2\)</blank>