The equation for the surface area of a cone is: [tex]SA = \pi r^{2} + \pi rl[/tex]
SA = surface area
r = radius
l = slant height
From the picture, you can see that the radius of the base of the cone, r=3mm. The slant height of the cone (length from base to the top point of the cone along the side of the code), l=12mm.
Plug these numbers into the equation for the surface area of a cone:
[tex]SA = \pi r^{2} + \pi rl\\
SA = \pi (3 \: mm)^{2} + \pi (3 \: mm)(12 \: mm)\\
SA = \pi ((3 \: mm)^{2} + (3 \: mm)(12 \: mm))\\
SA = \pi (9 \: mm^{2} + 36 \: mm^{2})\\
SA = 45\pi \:mm^{2} [/tex]
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Answer: C) 45π [tex]mm^{2} [/tex]
