To find the total surface area of this cone, we have that the total lateral area is given by the formula:
[tex]A_{\text{lateral}}=s\cdot\pi\cdot r[/tex]
Where
s is the slant height of the cone, s = 12 inches.
r is the radius of the base of the cone, r = 7 inches.
To that area, we need to add the area of the base of the cone:
[tex]A_{\text{base}}=\pi\cdot r^2[/tex]
That is, this is the area of a circle with this radius. Then, the total surface area is:
[tex]A_{\text{total}=}s\cdot\pi\cdot r+\pi\cdot r^2[/tex]
Substituting the values in this formula, we have:
[tex]A_{\text{total}}=12in\cdot3.14\cdot7in+\pi\cdot(7in)^2=263.76in^2_{}+153.86in^2[/tex]
Then
[tex]A_{\text{total}}=417.62in^2[/tex]
Hence, the total area is equal to 417.62 square inches.
