To solve this problem you must apply the proccedure shown below:
1. You must apply the formula for calculate the surface area of a cone, which is:
[tex] SA=\pi r^{2} +\pi rl [/tex]
Where [tex] r [/tex] is the radius ([tex] r=7cm [/tex]) and [tex] l [/tex] is the slant height ([tex] l=12cm [/tex]) and [tex] \pi =3.14 [/tex]
2. You need to substitute these values into the formula:
[tex] SA=(3.14) (7cm)^{2} +(3.14)(7cm)(12cm)\\ SA=417.62cm^{2} [/tex]
Therefore, the answer is the last option: [tex] 417.62cm^{2} [/tex]
