Cone measurements

Hi good people!,

I have something strange here...well, for me that is..

A cone with base radius = 6cm, perpendicular height (PH)  = 8cm. we are asked to calculate the volume of the cone. Using ${1 \over3 } \pi r^2*PH$  it calculates to 301,59 $cm^3$. The book gets 50,27 $cm^3$. When I look at the calc in the book, I notice they did not use $6^2$ for the radius but only 6. Surely that is an error on their part?

but what baffles me is that when I calculate the total outer area, using the slanted height (SH), which calculates to 10 cm (Having used Pythagoras), in this formula:

$\pi r^2 + \pi rSH$, it also calculates to 301,59 $cm^2$. 

would it be possible to please show me my error?...Thank you very much!