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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].
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].
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