The curved surface area of a cone is 670 ${\text{cm}}^{\text{2}}$ and its radius is 15 cm. Then its total surface area is

Given, curved surface area of cone $=670{\text{cm}}^{\text{2}}$

Radius $\left(r\right)=15\text{cm}$

Total surface area $=\text{C}\text{.S}\text{.A}+\left(\text{Area}\text{of}\text{base}\right)$

$=670+\frac{22}{7}\times 15\times 15$

$=670+\frac{4950}{7}$

$=670+707.14$

$=1377.14{\text{cm}}^2$