Question

select all the correct cylinders. which cylinders have a surface area of approximately 520 square units?

Explanation:

The surface area of a cylinder is given by the formula \( SA = 2\pi r^2 + 2\pi rh \), where \( r \) is the radius and \( h \) is the height. We'll calculate the surface area for each cylinder:

Step 1: Analyze the first cylinder (diameter = 12, height = 8)

• Radius \( r=\frac{12}{2} = 6 \)
• Height \( h = 8 \)
• Surface area \( SA = 2\pi(6)^2 + 2\pi(6)(8) \)
• \( SA = 2\pi(36) + 2\pi(48) \)
• \( SA = 72\pi + 96\pi = 168\pi \approx 168\times3.14 = 527.52 \approx 520 \) (close enough)

Step 2: Analyze the second cylinder (diameter = 4, height = 12)

• Radius \( r=\frac{4}{2}=2 \)
• Height \( h = 12 \)
• Surface area \( SA = 2\pi(2)^2 + 2\pi(2)(12) \)
• \( SA = 8\pi + 48\pi = 56\pi \approx 56\times3.14 = 175.84 \) (not ~520)

Step 3: Analyze the third cylinder (diameter = 8, height = 17)

• Radius \( r=\frac{8}{2}=4 \)
• Height \( h = 17 \)
• Surface area \( SA = 2\pi(4)^2 + 2\pi(4)(17) \)
• \( SA = 32\pi + 136\pi = 168\pi \approx 168\times3.14 = 527.52 \approx 520 \) (close enough)

Step 4: Analyze the fourth cylinder (diameter = 7, height = 5)

• Radius \( r=\frac{7}{2}=3.5 \)
• Height \( h = 5 \)
• Surface area \( SA = 2\pi(3.5)^2 + 2\pi(3.5)(5) \)
• \( SA = 24.5\pi + 35\pi = 59.5\pi \approx 59.5\times3.14 = 186.83 \) (not ~520)

Answer:

The cylinders with diameter 12 (radius 6) and height 8, and diameter 8 (radius 4) and height 17.