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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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