The lateral surface area of a cone can be calculated using the following formula:
[tex]L=\pi rl[/tex]Where "r" is the radius of the base and "l" is the slant height of the cone.
The total surface area of a cone can be found with this formula:
[tex]\begin{gathered} S=\pi rl+\pi r^2 \\ S=L+\pi r^2 \end{gathered}[/tex]Where "r" is the radius of the base and "L" is the lateral surface area of the cone.
In this case you know that the diameter of the base on the cone given in the exercise, is:
[tex]d=14in[/tex]Since the radius is half the diameter:
[tex]r=\frac{14in}{2}=7in[/tex]You know that the slant height is:
[tex]l=28in[/tex]Therefore, substituting values into the first formula and evaluating, you get that:
[tex]\begin{gathered} L=\pi(7in)(28in) \\ L\approx615.8in^2 \end{gathered}[/tex]And the total surface area is:
[tex]\begin{gathered} S=LSA+\pi r^2 \\ S=\pi(7in)(28in)+\pi(7in)^2 \\ S\approx769.7in^2 \end{gathered}[/tex]The answers are:
[tex]\begin{gathered} L=615.8in^2 \\ S=769.7in^2 \end{gathered}[/tex]
