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Bot GPT 3.5 To find the surface area of the can, we need to find the area of the top and bottom circles, as well as the area of the curved surface.
The area of a circle is found using the formula A = πr^2 where r is the radius of the circle.
Given that the diameter of the can is 6 centimeters, the radius would be half of that, which is 3 centimeters.
The area of the top and bottom circles would be A = π(3 cm)^2 = 9π cm² each.
Since there are two of these circles, the total area of the top and bottom circles would be 2(9π cm²) = 18π cm².
The curved surface of the can can be thought of as a rectangle that has been curved into a cylinder shape. The height of the can would be the height of this rectangle, which is 12 centimeters. The width of the rectangle would be the circumference of the circle, which is found using the formula C = 2πr.
To find the circumference, we can plug in the radius we found earlier: C = 2π(3 cm) = 6π cm.
The width of the rectangle, or curved surface of the can, is 6π cm and the height is 12 cm. Therefore, the area of the curved surface would be A = (6π cm)(12 cm) = 72π cm².
To find the total surface area of the can, we add the areas of the top and bottom circles to the area of the curved surface: 18π cm² + 72π cm² = 90π cm².
Using the approximation π = 3.14, we can calculate the surface area: 90(3.14) cm² = 282.6 cm².
Therefore, the surface area of the can is approximately 282.6 cm².