235.5 units^2 or 75π
Here is why:
The formula for the surface area of a cone is...
[tex]SA=\pi r^2+\pi rl[/tex]
Since you didn't specify if you wanted an exact or approximate answer, I will be doing both. The lateral height is l, so I'm going to assume the height you gave is the lateral height. We can now plug everything in.
[tex]SA=(3.14*5*5)+(3.14*5*10)[/tex]
[tex]SA=78.5+157[/tex]
[tex]SA=[/tex]
235.5
Now that we have the approximate answer, we will find the exact answer or the answer in pi.
[tex]SA=(\pi *5*5)+(\pi *5*10)[/tex]
[tex]SA=25\pi +50\pi[/tex]
[tex]SA=[/tex]
75π
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The approximate answer for the surface area of the cone is 235.5 units^2 and the answer in terms of pi is 75π.
