Question

Find the surface area. Leave your answers in terms of π.cones 1A. 65π ft²B. 90π ft²C. 32.5π ft²D. 105π ft²

Answer 1

For this problem, we need to calculate the surface area of a cone.

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

`A=\pi r(r+√(h^2+r^2))`

We need to determine the height of the cone, we can use Pythagora's theorem to determine the height:

`\begin{gathered} 13^2=h^2+5^2\\ \\ h^2=169-25\\ \\ h=√(144)=12 \end{gathered}`

Now we can determine the surface area:

`\begin{gathered} A=\pi\cdot5\cdot(5+√(12^2+5^2))\\ \\ A=\pi\cdot5\cdot(5+√(144+25))\\ \\ A=\pi\cdot5\cdot(5+√(169))\\ \\ A=\pi\cdot5\cdot(5+13)\\ \\ A=\pi\cdot5\cdot18\\ \\ A=90\pi \end{gathered}`

The correct answer is B, 90pi.