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Illustrative Math
Grade 8
Let’s figure out the dimensions of cones.
Illustrative Math Unit 8.5, Lesson 16 (printable worksheets)
The following diagram shows how to find missing information about a cone if I know its volume and some other information.
For each equation, decide what value, if any, would make it true.
The volume V of a cone with radius r is given by the formula V = 1/3πr^{2}h.
The volume of this cone with height 3 units and radius r is 64π cubic units. This statement is true:
64π = 1/3 πr^{2} · 3
What does the radius of this cone have to be? Explain how you know.
Each row of the table has some information about a particular cone. Complete the table with the missing dimensions.
A frustum is the result of taking a cone and slicing off a smaller cone using a cut parallel to the base.
Find a formula for the volume of a frustum, including deciding which quantities you are going to include in your formula.
Volume of frustum = volume of bigger cone - volume of smaller cone.
Quantities needed are the radius and height of the bigger cone and the radius and height of the smaller cone.
A movie theater offers two containers: Which container is the better value? Use 3.14 as an approximation for π.
The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics.
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