Explanation:
To figure out the lateral surface area of the cone, we will use the formula below
[tex]A_{lateral}=\pi rl[/tex]
To figure out the slant height l, we will use the formula below
[tex]\begin{gathered} l^2=5^2+6^2 \\ l^2=25+36 \\ l^2=61 \\ l=\sqrt{61} \end{gathered}[/tex]
By substituting the values, we will have
[tex]\begin{gathered} A_{lateral}=\pi rl \\ A_{lateral}=\pi\times6\times\sqrt{61} \\ A_{lateral}=147ft^2 \end{gathered}[/tex]
Hence,
The laterla surface area of the cone is
[tex]147ft^2[/tex]
Part B:
To calculate the value of the are of the sides and bottom of the cylinder, we will use the formula below
[tex]\begin{gathered} A_2=2\pi rh+\pi r^2 \\ where, \\ r=\frac{12}{2}ft=6ft \\ h=20ft \end{gathered}[/tex]
By substituting the values, we will have
[tex]\begin{gathered} A_{2}=2\pi rh+\pi r^{2} \\ A_2=2\pi\times6\times20+\pi\times6^2 \\ A_2=240\pi+36\pi \\ A_2=276\pi \\ A_2=867.08ft^2 \end{gathered}[/tex]
Hence,
The surface area of the sides and both if the cylinder is about
[tex]867ft^2[/tex]
Part C:
The total surface area of the of the figure wil be
[tex]\begin{gathered} 147ft^2+867ft^2 \\ 1014ft^2 \end{gathered}[/tex]
