# Surface area of a cone

*Here you'll learn how to calculate the surface area of a cone.*

As for volume of a cone, let's keep it simple and consider a right circular cone - one which has its apex directly above the center of its circular base.

What is the surface area of a cone?

The sum of the cone's circular base and curved surface areas.

Surface area of cone formula

**Cone surface area = circular base area + curved surface area**

If l = slant height and given a cone's base is circular and the area of a circle is πr² (where π= pi and r = radius of circle), the formula becomes

where SAcone = surface area of cone.

Example calculation

What's the surface area of a cone with base radius (r) 3cm
and slant height (l) 5cm (where cm = centimeters)?

SAcone

= πr² + πrl

= (π x 3²) + (π x 3 x 5)

= 75.4cm² (square centimeters) to 1 d.p. (one decimal place)

When working out the above, use the left and right bracket buttons on your calculator.

*The key stroke sequence is left bracket, pi sign (**π), multiply sign (x), 3, **squared sign (x**²), right bracket, multiply sign (x), left bracket, **pi sign (**π), multiply sign (x), 5, right bracket, *equals sign (=). Your calculator should display 75.39822369 which is 75.4 to 1 d.p. You may need to access *x**² and* *π* via a shift or 2nd function button.

## What if I only know the circular base radius (r) and perpendicular height (h)?

For instance, r = 3cm and h= 4cm.

Remember we're considering a right circular cone - the radius (r), perpendicular height (h) and slant height (l) form the sides of a right angle triangle, so the Pythagorean theorem can be applied.

l² = r² + h²

l = √ (r² + h²) = √ (3² + 4²) = √ (9 + 16) = √25 = 5cm

You can now enter r = 3cm and l = 5cm into the surface area of cone formula SAcone = πr² + πrl.

*Since the figures are the same as for the prior example calculation, you should get the answer 75.4cm² (square centimeters) to 1 d.p. (one decimal place).*

## Let's move on!

Click below for more cone geometry:

Volume of a cone

Related topics:

Volume of a cylinder

Surface area of a cylinder

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Surface area of a cone