Name:__________________ Date___
Popcorn Anyone?
Activity 1 – Partner 1 – Rectangular Prism
Problem: For this activity you will be comparing the volume of 2 rectangular
prisms. Each prism is created from an 8.5 inch by 11 inch of paper. You will be
determining whether:
 They both hold the same amount of popcorn, or
 The taller rectangular prism holds more popcorn, or
 The shorter rectangular prism holds more popcorn.
Objective: find a pattern for the dimensions for containers. Determine which shapes most likely
hold the largest volumes.
Materials:
 One piece each of white and colored 8.5 inch by 11 inch paper
 Tape
 Popcorn
 Plate
 Cup
 Ruler
STEP 1 – Identify the shape and volume formula
1. What is the name of the shape of the popcorn container pictured above?_________________
2. What is the formula to calculate the volume of this container? _________________
STEP 2: Create the containers
To create both rectangular prisms, you will use 2 sheets of paper. One sheet is plain and the other
is colored.
PLAIN
COLORED
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1. This is Rectangular Prism A: Take the plain piece of paper and fold it in half the long way.
Do this a 2nd time. You are forming a baseless rectangular prism that is tall and narrow.
Tape the edges and the middle. Do not overlap the sides. Measure the length, width and
height of each dimension with a ruler and record your data below and on the rectangular
prism:
Rectangular Prism A:
Length in inches:
Width in inches:
Height in inches:
2. This is Rectangular Prism B.: Now take the colored piece of paper and fold it in half the
wide way. Do this a 2nd time. You are forming another baseless rectangular prism that is
short and stout. Tape the edges and the middle. Do not overlap the sides. Measure the
length, width and height of each dimension with a ruler and record your data below and on
the rectangular prism:
Rectangular Prism B:
Length in inches:
Width in inches:
Height in inches:
3. Label your rectangular prism. Label the length, the width, and the height. And mark each
prism as Rectangular Prism A and Rectangular Prism B now to avoid confusion later.
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STEP 3: Create conjectures – which container will hold more popcorn?
Conjecture:
1. Do you think the two rectangular prisms will hold the same amount? ___________
2. Do you think one will hold more than the other? __________________________
Which one?_______________________________________________________
Why? __________________________________________________________
___________________________________________________________
STEP 4: Conduct the experiment:
Place rectangular prism B on the paper plate with rectangular prism A inside it. Use your cup to
pour popcorn into rectangular prism A. With care, slowly lift rectangular prism A so that the
popcorn falls into rectangular prism B.
 Is rectangular prism B full or overflowing?_____________________
As you share your popcorn snack, answer the questions below:
STEP 5: Analyzing results:
1. Was your prediction correct? ______________________
2. Do the two rectangular prisms hold the same amount? _________________
3. State the formula for finding the volume of a rectangular prism _________________________
4. Calculate the volume of Rectangular Prism A? Label the dimensions.
5. Calculate the volume of Rectangular Prism B? Label the dimensions.
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6. Explain why they do or do not hold the same amount. Think about how you folded the
rectangular prisms to guide your explanation.
7. What do you notice about the length and the width?
8. Rewrite the formula with only two variables to reflect this observation. Use s to represent the
smallest sides of the rectangular prisms.
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Activity 2 – Partner 2– Comparing Cylinders
Problem: For this activity you will be comparing the volume of 2
cylinders. Each cylinder is created from an 8.5 inch by 11 inch of
paper. You will be determining whether:
 They both hold the same amount of popcorn, or
 The taller cylinder holds more popcorn, or
 The shorter cylinder holds more popcorn.
Objective: find a pattern for the dimensions for containers.
Determine which shapes most likely hold the largest volumes.
Materials:
Same as listed for Activity 1.
STEP 1 – Identify the shapes and volume formula
1. What 2 shapes are parts of a cylinder?
A.
B.
2. What is the formula to calculate the volume of this container? _________________
STEP 2: Create the containers
To create both rectangular prisms, you will use 2 sheets of paper. One sheet is plain and the other
is colored.
PLAIN
COLORED
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1. This is Cylinder A: Take the plain piece of paper and roll it up along the longest side to form
a baseless cylinder that is tall and narrow. Tape the edges and the middle. Do not overlap
the sides. Record the height and calculate the radius based on the circumference.
Cylinder A:
Height of cylinder in inches:
Circumference of cylinder in
inches:
Radius of cylinder in inches:
2. This is Cylinder B: Take the colored piece of paper and roll it up along the shorter side to
form a baseless cylinder that is short and stout. Tape the edges and the middle. Do not
overlap the sides. Record the height and calculate the radius based on the circumference.
Height of cylinder in inches:
Circumference of cylinder in
inches:
Radius of cylinder in inches:
3. Label your cylinders. Label the diameter, radius, and the height. And mark each cylinder as
Cylinder A and Cylinder B now to avoid confusion later.
STEP 3: Create conjectures – which container will hold more popcorn?
Conjecture:
1. Do you think the two cylinders will hold the same amount? ___________
2. Do you think one will hold more than the other? __________________________
Which one?_______________________________________________________
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Why? __________________________________________________________
___________________________________________________________
STEP 4: Conduct the experiment:
Place cylinder B on the paper plate with cylinder A inside it. Use your cup to pour popcorn into
cylinder A. With care, slowly lift cylinder A so that the popcorn falls into cylinder B.
 Is cylinder B full or overflowing? _____________________
As you share your popcorn snack, answer the questions below:
STEP 5: Analyzing results:
1. Was your prediction correct? ______________________
2. Do the two cylinders hold the same amount? _________________
3. State the formula for finding the volume of a cylinder _________________________
4. Calculate the volume of Cylinder A? Label the dimensions.
5. Calculate the volume of Cylinder B? Label the dimensions.
6. Explain why they do or do not hold the same amount. Use the formula for the volume of a
cylinder to guide your explanation.
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7. Which measurement impacts the volume more; the radius or the height? Work through the
example below to help you answer the question.
Assume that you have a cylinder with a radius of 3 inches and a height of 10 inches. Increase
the radius by 1 inch and determine the new volume. Then using the original radius, increase
the height by 1 inch and determine the new volume. Which had a larger impact?
Original
Increased radius
Increased height
Radius
3
Height
10
Volume
Create another scenario and see if this follows a pattern.
Why do you think this is true?
Do you see a pattern?
Is there any observation you can make about tall shapes versus shapes with dimensions that are
closer? Support your observation with the results from the experiments with both rectangular
prisms and cylinders.
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