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Find the slant height of the cone as well as its lateral and surface area.
You'll need slant height to find the areas anyway. The Pythagorean Theorem is the way to go.
Slant height = 85 mm; L ≈ 3471 mm2; SA ≈ 4002 mm2
Find the surface area of the figure.
The surface area of the figure equals the lateral areas of the cone and the cylinder plus one base.
SA ≈ 4528 units2
Find the surface area of this figure.
The surface area of the top of the rectangular prism can be calculated by subtracting the circular base of the cylinder from the base of the rectangular prism. Everything else should be straightforward.