Arc Length, Sector Area, and Volume Introduction

What's the area of your slice of pizza? How many inches of crust does it have, and how does that relate to the total amount of crust around the whole pizza? How much ice cream does your waffle cone hold? How much oil can fit in each barrel? If you drink a full glass of water, how much did you drink? If you slice a pyramid horizontally at any point, what shape will you get? Believe it or not, these are all questions about area and volume that can be answered with the tools you will gain within this module!

Essential Questions

How can we show that the length of the arc intercepted by a given angle is proportional to the radius of the circle?
What is the formula for finding the area of a sector?
What are the formulas for finding the circumference and area of a circle and how can we use them?
What is Cavalier's principle and how can we use it to find the volume of a cylinder, pyramid, cone, sphere, and other prisms?
How can we identify the shape of a cross section of a three-dimensional object?
What types of three-dimensional shapes can be created by rotating a two-dimensional object about an axis?

Key Terms

Arc length - a portion of the circumference of a circle

Arc measure - the degree measure of the central angle that subtends the given arc

Sector area - a portion of the area of a circle

Central angle - an angle whose vertex is at the center of a circle

Radian - an angle measure which spans an arc length equal to the radius of the circle

Compass - an instrument for drawing circles and arcs and measuring distances between points, consisting of two arms linked by a movable joint, one arm ending in a point and the other usually carrying a pencil or pen

image of compass

Protractor - an instrument for measuring angles, typically in the form of a flat semicircle marked with degrees along the curved edge

image of protractor

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