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Bot GPT 3.5 To find the surface area of a cylinder, we need to find the lateral surface area and add the area of the two bases.
Let's start with Cylinder A:
- Radius = 15 inches
- Height = 22 inches
Lateral Surface Area of Cylinder A:
= 2 * π * radius * height
= 2 * 3.14 * 15 * 22
= 2079.6 square inches
Base Area of Cylinder A:
= π * (radius^2)
= 3.14 * (15^2)
= 706.5 square inches
Total Surface Area of Cylinder A:
= Lateral Surface Area + 2 * Base Area
= 2079.6 + 2 * 706.5
= 3492.6 square inches
Next, let's calculate for Cylinder B:
- Radius = 14 inches
- Height = 23 inches
Lateral Surface Area of Cylinder B:
= 2 * π * radius * height
= 2 * 3.14 * 14 * 23
= 2033.12 square inches
Base Area of Cylinder B:
= π * (radius^2)
= 3.14 * (14^2)
= 615.44 square inches
Total Surface Area of Cylinder B:
= Lateral Surface Area + 2 * Base Area
= 2033.12 + 2 * 615.44
= 3264 square inches
Lastly, let's find the Surface Area of Cylinder C:
- Diameter = 24 inches (Radius = 12 inches)
- Height = 21 inches
Lateral Surface Area of Cylinder C:
= 2 * π * radius * height
= 2 * 3.14 * 12 * 21
= 1581.12 square inches
Base Area of Cylinder C:
= π * (radius^2)
= 3.14 * (12^2)
= 452.16 square inches
Total Surface Area of Cylinder C:
= Lateral Surface Area + 2 * Base Area
= 1581.12 + 2 * 452.16
= 2485.44 square inches
Comparing the Total Surface Areas of the three cylinders:
- Cylinder A: 3492.6 square inches
- Cylinder B: 3264 square inches
- Cylinder C: 2485.44 square inches
Therefore, Cylinder A has the greatest surface area, making it the best choice for Justine to buy if she wants to justify her purchase based on maximum surface area.