Question

Find the total surface area of this cone.Leave your answer in terms of n.25 m8m=SA = [ ? ]7 m2ㅠHint: Surface Area of a Cone = tre + BWhere e = slant height, and B = area of the base

Answer 1

The surface area of a cone can be found through the formula:

`\begin{gathered} SA=\pi\ast r\ast\lambda+B \\ Where\text{ }\lambda\text{ is the slant height and B is the area of the base.} \\ since\text{ the base is a circle:} \\ B=\pi\ast r^2 \\ The\text{ resulting equation is:} \\ SA=\pi\ast r\ast\lambda+\pi\ast r^2 \\ Taking\text{ the common factor:} \\ SA=\pi\ast(r\lambda+r^2) \end{gathered}`

Using the given numbers

`\begin{gathered} SA=\pi\ast(25\ast8+8^2) \\ SA=\pi\ast(200+64) \\ SA=264\pi\text{ m}^2 \end{gathered}`

Answer:

The surface area of the cone is 264πm²