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Illustrative Math
Grade 8
Let’s figure out the dimensions of cylinders.
Illustrative Math Unit 8.5, Lesson 14 (printable worksheets)
In an earlier lesson we learned that the volume, V, of a cylinder with radius r and height h is
V = πr^{2}h
We say that the volume depends on the radius and height, and if we know the radius and height, we can find the volume. It is also true that if we know the volume and one dimension (either radius or height), we can find the other dimension.
For example, imagine a cylinder that has a volume of 500π cm^{3} and a radius of 5 cm, but the height is unknown. From the volume formula we know that
500π = π · 25 · h
must be true. Looking at the structure of the equation, we can see that 500 = 25h. That means that the height has to be 20 cm, since 500 ÷ 25 = 20.
Now imagine another cylinder that also has a volume of 500π cm^{3} with an unknown radius and a height of 5 cm. Then we know that
500π = π · r^{2} · 5
must be true. Looking at the structure of this equation, we can see that r^{2} = 100. So the radius must be 10 cm.
What is a possible volume for this cylinder if the diameter is 8 cm? Explain your reasoning.
The volume V of a cylinder with radius r is given by the formula V = πr^{2}h.
Suppose a cylinder has a volume of 36π cubic inches, but it is not the same cylinder as the one you found earlier in this activity.
Any combination of r^{2}h = 36
Example:
r = 2, h = 9
r = 3, h = 4
There would be an infinite number of different cylinders since r and h need not be whole numbers.
Each row of the table has information about a particular cylinder. Complete the table with the missing dimensions.
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