Illustrative Mathematics Grade 8, Unit 5, Lesson 16: Finding Cone Dimensions

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Illustrative Math
Grade 8

Lesson 16: Finding Cone Dimensions

Let’s figure out the dimensions of cones.

Illustrative Math Unit 8.5, Lesson 16 (printable worksheets)

Lesson 16 Summary

The following diagram shows how to find missing information about a cone if I know its volume and some other information.

Lesson 16.1 Number Talk: Thirds

For each equation, decide what value, if any, would make it true.

• See Video for Whole Lesson

Lesson 16.2 An Unknown Radius

The volume V of a cone with radius r is given by the formula V = 1/3πr²h.
The volume of this cone with height 3 units and radius r is 64π cubic units. This statement is true:
64π = 1/3 πr² · 3
What does the radius of this cone have to be? Explain how you know.

Lesson 16.3 Cones with Unknown Dimensions

Each row of the table has some information about a particular cone. Complete the table with the missing dimensions.

Are you ready for more?

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.

• Show Answer

  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.

Popcorn Deals

A movie theater offers two containers: Which container is the better value? Use 3.14 as an approximation for π.

Lesson 16 Practice Problems

1. The volume of this cylinder is 175π cubic units.
   What is the volume of a cone that has the same base area and the same height?
2. A cone has volume 12π cubic inches. Its height is 4 inches. What is its radius?
3. A cone has volume 3π.
   a. If the cone’s radius is 1, what is its height?
   b. If the cone’s radius is 2, what is its height?
   c. If the cone’s radius is 5, what is its height?
   d. If the cone’s radius is 1/2, what is its height?
   e. If the cone’s radius in r, then what is the height?
4. Three people are playing near the water. Person A stands on the dock. Person B starts at the top of a pole and ziplines into the water. Person C climbs out of the water and up the zipline pole. Match the people to the graphs where the horizontal axis represents time in seconds and the vertical axis represents height above the water level in feet.
5. A room is 15 feet tall. An architect wants to include a window that is 6 feet tall. The distance between the floor and the bottom of the window is b feet. The distance between the ceiling and the top of the window is a feet. This relationship can be described by the equation
   a = 15 - (b + 6)
   a. Which variable is independent based on the equation given?
   b. If the architect wants b to be 3, what does this mean? What value of a would work with the given value for b?
   c. The customer wants the window to have 5 feet of space above it. Is the customer describing a or b? What is the value of the other variable?

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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