Cone Study Guide

A cone is a three-dimensional geometric shape that tapers smoothly from a flat, usually circular base to a point called the apex or vertex. Here are some key points to remember about cones:

Base: The base of a cone is a circular flat surface.
Vertex: The vertex is the point at the top of the cone where the sides meet.
Height: The height of a cone is the perpendicular distance from the base to the vertex.
Slant Height: The slant height is the distance from the vertex to any point on the edge of the base, measured along the curved surface.
Surface Area: The surface area of a cone can be calculated using the formula: SA = πr(r + l), where r is the radius of the base and l is the slant height.
Volume: The volume of a cone can be calculated using the formula: V = (1/3)πr²h, where r is the radius of the base and h is the height.

Now that you have a basic understanding of cones, it's important to practice using the formulas to solve problems. Here are some practice questions for you:

Calculate the surface area of a cone with a radius of 5 cm and a slant height of 8 cm.
Find the volume of a cone with a radius of 4 in and a height of 10 in.
If the slant height of a cone is 12 m and the radius of the base is 6 m, what is the surface area?

Remember to always include the units in your answers and round to the appropriate decimal places!