History for Kids Geography for kids Science for kids Kids Educational Site and Search Study and Homework for kids Sports Games
advertisement

Kids Math

Finding the Volume and
Surface Area of a Cone

What is a cone?

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 + πr2


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?

Surface area = πrs + πr2
= (3.14x4x8) + (3.14x4x4)
= 100.48 + 50.24
= 150.72 cm2


Volume of a Cone

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 = 1/3πr2h


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 = 1/3πr2h
= 3.14 x 4 x 4 x 7 ÷ 3
= 117.27 cm 3


Things to Remember
  • Surface area of a cone = πrs + πr2
  • Volume of a cone = 1/3πr2h
  • 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.



More Geometry Subjects

Circle
Polygons
Quadrilaterals
Triangles
Pythagorean Theorem
Perimeter
Slope
Surface Area
Volume of a Box or Cube
Volume and Surface Area of a Sphere
Volume and Surface Area of a Cylinder
Volume and Surface Area of a Cone
Angles glossary
Figures and Shapes glossary


Back to Kids Math

Back to Kids Study

Kid's Poll



More polls











Privacy Policy

Kids Games  History for Kids  Homework Help  Science  Geography for Kids 

About Ducksters  Link to Ducksters  Teachers 

Last updated: This site is a product of TSI (Technological Solutions, Inc.), Copyright 2014, All Rights Reserved. By using this site you agree to the Terms of Use.


To cite this article using MLA style citation: