Sure! Let's break this down step by-step.
1. Given Measurements:
- Diameter of the base of the cylinder: [tex]\(d = 8 \text{ inches}\)[/tex]
- Height of the cylinder: [tex]\(h = 5 \text{ inches}\)[/tex]
2. Calculate the Radius:
- The radius [tex]\(r\)[/tex] of the base of the cylinder is half of the diameter.
[tex]\[
r = \frac{d}{2} = \frac{8}{2} = 4 \text{ inches}
\][/tex]
3. Formula for Surface Area of a Cylinder:
- The surface area [tex]\(A\)[/tex] of a cylinder is given by the formula:
[tex]\[
A = 2\pi r (r + h)
\][/tex]
- Where:
- [tex]\(\pi\)[/tex] (pi) is approximately 3.141592653589793
- [tex]\(r\)[/tex] is the radius
- [tex]\(h\)[/tex] is the height
4. Substitute the Values:
[tex]\[
A = 2\pi (4) (4 + 5)
\][/tex]
[tex]\[
A = 2\pi (4) (9)
\][/tex]
[tex]\[
A = 2\pi \times 36
\][/tex]
[tex]\[
A = 72\pi
\][/tex]
5. Include the Units:
- The surface area is measured in square inches ([tex]\(\text{in}^2\)[/tex])
So, the surface area of the cylinder is:
[tex]\[
72\pi \text{ in}^2
\][/tex]
To summarize, the surface area of a cylinder with a base diameter of 8 inches and a height of 5 inches is [tex]\(72\pi \text{ in}^2\)[/tex].
