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We see this is a cylinder with total surface area = 461.8 sq. mm.

Diameter 14 mm.

Surface Area = (base area) + (base area) + (lateral area)

Surface Area = (pi * r*r) + (pi * r*r) + ( pi*d * h)

where r = radius of circle base, d = diameter of the circle base

and h = height of the cylinder.

d = 14 mm. then the radius is half of the diameter, so r = 7 mm.

Plug it into the formula

461.8 = 3.1415926* 7*7 + 3.1415926*7*7 + 3.1415926*14*h

461.8 = 307.87608 + 43.98229 * h

153.92392/ 43.98229 = h

h = 3.4996 mm.

Answer Choice C.) 3.5 mm.

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