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Cones

Study Guide

Key Definition

A cone is a solid composed of a circle (base), a given point not on the plane of the circle (vertex) and all the segments from the point to the circle. There are formulas about cones that are related to pyramids.

Important Notes

  • The radius of the cone is the radius of the base
  • The height of the cone is the length of the altitude
  • The slant height is not defined for oblique cones. For oblique cones, use the generator length at a stated point instead

Mathematical Notation

$\pi r l$ is the formula for the lateral surface area of a right coneRemember to use proper notation when solving problems

Why It Works

A cone is closely related to a pyramid. Hence, the formulas for their surface areas and volume are related.

Remember

The base of a cone is a circle, hence we can apply circle formulas when solving problems involving cones.

Quick Reference

Lateral Surface Area of a Cone:$\pi r l$Total Surface Area of a Cone:$\pi r l + \pi r^2$Volume of a Cone:$(1/3)\pi r^2 h$

Understanding Cones

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Beginner Explanation

A cone is a solid shape with a circle base and a point, called a vertex. The radius is the distance from the center of the base to the edge. The height is the distance from the base to the vertex.Now showing Beginner level explanation.

Practice Problems

Test your understanding with practice problems

1

Quick Quiz

Single Choice QuizBeginner

What is the formula for the lateral surface area of a right cone?

A$\pi r^2$B$\pi r l$C$\pi r^2 h$D$2 \pi r$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.2

Real-World Problem

Question ExerciseIntermediate

Ice Cream Cone

You have an ice cream cone with radius 2 inches and slant height 5 inches (the 5-inch measure is the slant height). How much waffle does the ice cream shop need to make the cone?Show AnswerClick to reveal the detailed solution for this question exercise.3

Thinking Challenge

Thinking ExerciseIntermediate

Think About This

Why is the slant height not defined for oblique cones?

Show AnswerClick to reveal the detailed explanation for this thinking exercise.

Recap

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Review key concepts and takeaways

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