Question

Hello I need help on question #6… for geometry please. This is a practice sheet.

Answer 1

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-

`\begin{gathered} A=\pi r^2+\pi rl \\ or, \\ A=\pi r(l+r) \end{gathered}`

Given,

`\begin{gathered} r=(16)/(2) \\ r=8\text{ in} \\ l=17\text{ in} \end{gathered}`

Hence, the surface area of the cone is

`\begin{gathered} A=\pi*8*(17+8) \\ A=8\pi*25 \\ A=200\pi \end{gathered}`

Or,

`A=628.57\text{ in}^2`

Final Answer: The given figure is a cone with a surface area of 628.57 square inches.