Given: A figure with a diameter of 16 in and a slant height of 17 in.
Required: To name the figure and find out the surface area of the given figure.
Explanation: The given figure is a cone. The surface area of a cone with radius 'r' and slant height 'l' is given by the formula-
[tex]\begin{gathered} A=\pi r^2+\pi rl \\ or, \\ A=\pi r(l+r) \end{gathered}[/tex]
Given,
[tex]\begin{gathered} r=\frac{16}{2} \\ r=8\text{ in} \\ l=17\text{ in} \end{gathered}[/tex]
Hence, the surface area of the cone is
[tex]\begin{gathered} A=\pi\times8\times(17+8) \\ A=8\pi\times25 \\ A=200\pi \end{gathered}[/tex]
Or,
[tex]A=628.57\text{ in}^2[/tex]
Final Answer: The given figure is a cone with a surface area of 628.57 square inches.
