A cone is a type of geometric shape. There are different kinds of cones. They all have a flat surface on one side that tapers to a point on the other side.
We will be discussing a right circular cone on this page. This is a cone with a circle for a flat surface that tapers to a point that is 90 degrees from the center of the circle.
Terms of a Cone
In order to calculate the surface area and volume of a cone we first need to understand a few terms:
Radius - The radius is the distance from the center to the edge of the circle at the end.
Height - The height is the distance from the center of the circle to the tip of the cone.
Slant - The slant is the length from the edge of the circle to the tip of the cone.
Pi - Pi is a special number used with circles. We will use an abbreviated version where Pi = 3.14. We also use the symbol π to refer to the number pi in formulas.
Surface Area of a Cone
The surface area of a cone is the surface area of the outside of the cone plus the surface area of the circle at the end. There is a special formula used to figure this out.
Surface area = πrs + πr^{2}
r = radius
s = slant
π = 3.14
This is the same as saying (3.14 x radius x slant) + (3.14 x radius x radius)
Example:
What is the surface area of a cone with radius 4 cm and slant 8 cm?
There is special formula for finding the volume of a cone. The volume is how much space takes up the inside of a cone. The answer to a volume question is always in cubic units.
Volume = 1/3πr^{2}h
This is the same as 3.14 x radius x radius x height ÷ 3
Example:
Find the volume of a cone with radius 4 cm and height 7 cm?
Volume = 1/3πr^{2}h
= 3.14 x 4 x 4 x 7 ÷ 3
= 117.23 cm ^{3}
Things to Remember
Surface area of a cone = πrs + πr^{2}
Volume of a cone = 1/3πr^{2}h
The slant of a right circle cone can be figured out using the Pythagorean Theorem if you have the height and the radius.
Answers for volume problems should always be in cubic units.
Answers for surface area problems should always be in square units.