Given:
Radius of cone, r = 12 cm
Slant height, L = 28 cm
Let's find the lateral area and surface area of the cone.
Lateral area:
To find the lateral area of the cone, apply the formula:
[tex]A=\pi rl[/tex]Thus, we have:
[tex]\begin{gathered} A=\pi\ast12\ast28 \\ \\ A=\pi\ast336 \\ \\ \text{ A = }1055.575cm^2 \end{gathered}[/tex]Solving further:
Therefore, the lateral area is 1055.575 square centimeters.
Surface Area:
To find the surface area, apply the formula
[tex]SA=\pi rl+\pi r^2[/tex]We have:
[tex]SA=(\pi\ast12\ast28)+(\pi\ast12^2)[/tex]Solving further:
[tex]\begin{gathered} SA=(1055.575)+(452.389) \\ \\ \text{ SA=1507.964 cm}^2 \end{gathered}[/tex]Therefore, the surface area is 1507.964 square centimeters.
ANSWER:
Lateral area = 1055.575 cm²
Surafce area = 1507.964 cm²
