The surface area of the cone equals the area of

the circle plus the
area of the cone. To find the surface area of a cone, find the area of the circle and area of the cone.

**Steps for finding the Surface Area of a Cone:**

Step 1: Measure the radius or slant height of the cone.(If not given)

Step 2: Find the area of the circle or base of the cone (using formula A = $\pi r^2$).

Step 3: Find the area of a cone($\pi$ r l) by measuring its slant height. (Make sure you use the same form of measurement as the radius).

Step 4: Write answer in the proper square unit of measurement.

Example:The height of a

circular cone is 15 inches and the radius of the base is 20 inches. What is the surface area of the cone ?

Solution:

GivenHeight of a cone (h) = 15 inches

Radius of the cone (r) = 20 inches

Surface area of the cone (SA) = ?

Step 1:Find the slant height of the cone:

We know that,

l^{2} = r^{2} + h^{2} => l

^{2} = (20)

^{2} + (15)

^{2} => l

^{2} = 400 + 225

=> l

^{2} = 625

or

** l = 25**

Step 2:Area of the circle:

Area of the circle = $\pi r^2$= $\pi$ (20)

^{2}= 400 $\pi$

=>

** Area of the circle = 400 $\pi$**

Step 3:

Find the area of a cone:

Area of the cone = $\pi$ r l

=> Area of the cone = $\pi$ * 20 * 25

= 500 $\pi$

=>

**Area of the cone = 500 $\pi$**

Step 4:

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

or Surface Area of a Cone = $\pi$ r

^{2} + $\pi$ rl

= 400 $\pi$ + 500$\pi$

= (400 + 500)$\pi$

= 900 $\pi$

Hence the surface area of a cone = 900 $\pi$ inches

^{2} .