Answer Key – Ice Cream Puddle
1.
Squish the spherical modeling clay to form a circular puddle. (a) What 3-dimensional figure
are you forming? (b) How does squishing the clay compare to ice cream melting? (c)
Measure your squished clay figure and calculate its volume. Compare your answer to the
volume of the sphere you started with.
(a) The clay makes a cylinder with a very small height.
(b) The ice cream cone puddle would have less depth, even if you were to use a
rolling pin to roll out the clay.
(c) Answers will vary. However, the volume of the cylinder should be close to
(due to measurement errors. In theory, they would be equal) the volume of the
original sphere.
2. Explain how you decided the actual dimensions of the ice cream cone shown in the picture
and what units to use.
Answers will vary. Sample answer: I used the height of the door to approximate the
height of each scoop, the height of the cone, and the diameter of the cone’s base.
3. Before the ice cream started melting, how many scoops were there? What does this say about
the kinds of formulas we might want to use?
If they assume only four scoops, the only formula used would be the volume of a
sphere or hemisphere.
4. How did you decide how much ice cream was in the cone? What does this say about the
kinds of formulas we might want to use?
If students assume some ice cream is inside the cone, they would also need to use
the formula for the volume of a cone and add to it the volume of a sphere or
hemisphere.
5. How can you use the answer from the problem with the small cone and clay to make a better
estimate for the diameter of the puddle that would be produced by the giant ice cream cone
sculpture?
Answers will vary. Sample solution: Students may decide that their estimate of
the puddle diameter for the ice cream cone sculpture was not very accurate or they
can write about finding the ratio between the model and photo to determine
whether their calculations produce a reasonable result.
6. What factors might cause the actual size of the puddle to be different from the estimate?
The cone may not have been completely filled, the scoop was not a perfect sphere,
the radius of the scoop may not have been the same as that of the cone, etc.
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