If the curved surface area of a right circular cone is $3080\text{sq cm}$ and its slant height is $35\text{cm}$, find its total surface area.

Given:Curved Surface Area ($\text{CSA}$) = $3080\text{sq cm}$ Slant height ($l$) = $35\text{cm}$ The formula for the curved surface area of a cone is:
$$\text{CSA}=\pi rl$$
Where $r$ is the radius of the base.Substitute the values:
$$3080=\frac{22}{7}\times r\times 35$$
$$3080=22\times r\times 5$$
$$3080=110\times r$$
$$r=\frac{3080}{110}=28\text{cm}$$
The formula for the Total Surface Area ($\text{TSA}$) of a cone is:
$$\text{TSA}=\text{CSA}+\text{Base Area}=\pi rl+\pi r^2=\pi r(l+r)$$
Substitute the known parameters ($r=28\text{cm}$, $l=35\text{cm}$):
$$\text{TSA}=\frac{22}{7}\times 28\times (35+28)$$
$$\text{TSA}=22\times 4\times 63$$
$$\text{TSA}=88\times 63=5544\text{sq cm}$$