Like a pyramid, a cone is a solid that has one base and a vertex that is not in the same plane as the base. However, the base of a cone is a circle. In a right cone, the altitude is a perpendicular segment from the vertex to the center of the base. The height h is the length of the altitude. The slant height l is the distance from the vertex to a point on the edge of the base. In this book, you can assume that a cone is a right cone unless stated or pictured otherwise.
The lateral area is half the circumference of the base times the slant height. The formulas for the lateral area and surface area of a cone are similar to those for a pyramid.
Take note Theorem 11-4: Lateral and Surface Areas of a Cone
The lateral area of a right cone is half the product of the circumference of the base and the slant height of the cone.
The surface area of a cone is the sum of the lateral area and the area of the base.
Problem 3 Finding the Surface Area of a Cone
What is the surface area of the cone in terms of
Think
How is this different from finding the surface area of a pyramid?
For a pyramid, you need to find the perimeter of the base. For a cone, you need to find the circumference.
The surface area of the cone is
✓ Got It?
- The radius of the base of a cone is 16 m. Its slant height is 28 m. What is the surface area in terms of
By cutting a cone and laying it out flat, you can see how the formula for the lateral area of a cone (
Table of Contents
- 6-1 The Polygon Angle-Sum Theorems
- 6-2 Properties of Parallelograms
- 6-3 Proving That a Quadrilateral Is a Parallelogram
- 6-4 Properties of Rhombuses, Rectangles, and Squares
- 6-5 Conditions for Rhombuses, Rectangles, and Squares
- 6-6 Trapezoids and Kites
- 6-7 Polygons in the Coordinate Plane
- 6-8 and 6-9 Coordinate Geometry and Coordinate Proofs