Answer
Explanation
Background
• Diameter: ,line that touches two opposite points in a circumference and passes through the center of the circle.
,
• Radius: ,the distance from the center to any point in the circumference. Also, it is half the diameter.
The surface area (SA) of a cylinder is given by:
[tex]SA=2\pi r^2+2\pi rh[/tex]
where r represents the radius and h represents the height.
Based on the given figures, we can conclude that:
• The cylinder in the upper left corner has a diameter of 12 and a height of 8, meaning r = 12/2 = 6 and h = 8.
• The cylinder in the upper right corner has a radius of 2 and a height of 12, meaning r = 2 and h = 12.
• The cylinder in the lower right corner has a radius of 7 and a height of 5, meaning r = 7 and h = 5.
• The cylinder in the lower left corner has a diameter of 8 and a height of 17, meaning r = 8/2 = 4 and h = 17.
Now, we can replace these values in the formula:
• Cylinder in the upper left corner
[tex]SA=2\pi(6)^2+2\pi(6)(8)[/tex][tex]SA=2\pi(36)+2\pi(48)[/tex][tex]SA=72\pi+96\pi[/tex][tex]SA=168\pi\approx527.78\approx528[/tex]
• Cylinder in the upper right corner
[tex]SA=2\pi(2)^2+2\pi(2)(12)[/tex][tex]SA=8\pi+48\pi=56\pi[/tex][tex]SA=56\pi\approx175.93\approx176[/tex]
• Cylinder in the lower right corner
[tex]SA=2\pi(7)^2+2\pi(7)(5)[/tex][tex]SA=98\pi+70\pi=168\pi\approx528[/tex]
• Cylinder in the lower left corner
[tex]SA=2\pi(4)^2+2\pi(4)(17)[/tex][tex]SA=32\pi+1362\pi=168\pi\approx528[/tex]
