To find the surface area of a cylinder with a base diameter of 6 feet and a height of 5 feet, let's follow a step-by-step approach:
1. Understand the given values:
- Diameter of the base ([tex]\(d\)[/tex]): 6 feet
- Height of the cylinder ([tex]\(h\)[/tex]): 5 feet
2. Calculate the radius ([tex]\(r\)[/tex]) of the base:
- The radius is half the diameter.
[tex]\( r = \frac{d}{2} = \frac{6 \text{ feet}}{2} = 3 \text{ feet} \)[/tex]
3. Surface area of a cylinder:
The surface area ([tex]\(A\)[/tex]) of a cylinder consists of two parts:
- The lateral surface area
- The area of the two circular bases
4. Calculate the lateral surface area:
- The formula to calculate the lateral surface area is [tex]\(2 \pi r h\)[/tex].
- Substituting the known values:
[tex]\( 2 \pi \times 3 \text{ feet} \times 5 \text{ feet} = 30 \pi \text{ square feet} \)[/tex]
5. Calculate the area of one base:
- The area of a circle is given by [tex]\(\pi r^2\)[/tex].
- Substituting the known value of the radius:
[tex]\( \pi \times (3 \text{ feet})^2 = 9 \pi \text{ square feet} \)[/tex]
6. Calculate the area of both bases:
- A cylinder has two bases, so the total area of the bases is [tex]\(2 \pi r^2\)[/tex].
- Substituting the values:
[tex]\( 2 \times 9 \pi \text{ square feet} = 18 \pi \text{ square feet} \)[/tex]
7. Find the total surface area:
- The total surface area is the sum of the lateral surface area and the area of the two bases.
- Therefore:
[tex]\( \text{Total Surface Area} = 30 \pi \text{ square feet} + 18 \pi \text{ square feet} \)[/tex]
[tex]\( \text{Total Surface Area} = 48 \pi \text{ square feet} \)[/tex]
Thus, the surface area of the cylinder in terms of [tex]\(\pi\)[/tex] is:
[tex]\[ 48 \pi \text{ square feet} \][/tex]
