The total surface area of a cone is the sum of the area of its base and the lateral or side surface. The lateral surface area of a cone is the area of the lateral or side surface only. If a cone of radius 'r' and slant height 'l' is cut along the slant height and opened out flat then radius of the sector formed is 'l' and the arc length AB is circumference of the circle (2$\pi$r).

Total surface area of the cone = Area of the base + Area of curved surface

=> TSA = $\pi r^2$ + $\pi$rl

=> TSA = $\pi$ r(r + l)

**Formula:**

Total Surface Area of a Cone ( TSA) = $\pi$ r(r + l)

Where,

'r' is the radius and 'l' is the slant height of a cone.

Example:Find the total surface area of a cone if its slant
height is four times the radius, and base diameter of the
cone is 10 cm.

**Solution:**

GivenDiameter of the cone = 10 cm

Slant height of the cone = 4(Radius)

Step 1:Radius of the cone (r) =

$\frac{10}{2}$ = 5 cm

Slant height of the cone (l) = 4 * 5 = 20 cm

Step 2:

Total Surface Area of a Cone ( TSA) = $\pi$ r(r + l)=> TSA =

$\frac{22}{7}$ * 5(5 + 20)

=

$\frac{22}{7}$ * 5 * 25

= 392.85

Hence the total surface area of a cone is 392.85 cm

^{2} .