To calculate the surface area of a cone we can use the following formula:
![S=\pi r^2+\pi Lr](https://img.qammunity.org/2023/formulas/mathematics/college/90k21iyjcmp73sm04xpcc5ekigeajxphg6.png)
where r represents the radius of the base and L represents the slant height.
The radius of our cone is 7cm and the slant height 19cm, using those values on the formula we have our answer:
![S=\pi(7)^2+\pi(19)(7)=49\pi+133\pi=182\pi\approx571.8](https://img.qammunity.org/2023/formulas/mathematics/college/45ache1ne6wu56f2snxph6mel2a275c8xj.png)
The surface area of this cone is 571.8 cm².