Answer:
628.0 mm²
Step-by-step explanation:
The total surface area of the figure is the sum of the inside lateral area, the outside lateral area, and the area of the donut bases.
Lateral area
The lateral area of a cylinder is ...
A = 2πrh
The total lateral area of the inside and outside cylinders is ...
A = 2π(r1)h +2π(r2)h = 2π(r1 +r2)h
A = 2(3.14)(3 mm +7 mm)(6 mm) = 376.8 mm²
Base area
The area of one donut base is the product of the centerline length and the width.
A = πdw = (3.14)(7 mm +3 mm)(4 mm) = 125.6 mm²
Total area
The total surface area of the composite figure is the sum of its lateral area and the area of the two bases.
surface area = 376.8 mm² +2×125.6 mm² = 628.0 mm²
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Additional comment
The radius of the centerline of the base donut is the average of the inside and outside radii: half their sum. The diameter of the centerline circle is twice that average radius, so is equal to the sum of the inside and outside radii. This is the value we used above.
The width of the donut is the difference in the radii.
The product of the sum and difference is the same as the difference of the squares of the radii. That difference of squares would be what you have if you compute the overall area and subtract the inner area.
