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Solve each equation mentally.
The volume of a cone with radius is given by the formula .
This cone has a height 3 units and radius units.
The volume of this cone is given by the equation cubic units.
This statement is true:
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.
| diameter (units) | radius (units) | area of the base (square units) | height (units) | volume of cone (cubic units) | |
|---|---|---|---|---|---|
| a | 4 | 3 | |||
| b | 8 | ||||
| c | |||||
| d | 20 | ||||
| e | 6 | ||||
| f | 3 |
A movie theater offers two containers:
Which container is the better value? Use 3.14 as an approximation for .
As we saw with cylinders, the volume of a cone depends on the radius of the base and the height :
If we know the radius and height, we can find the volume. If we know the volume and one of the dimensions (either radius or height), we can find the other dimension.
For example, imagine a cone with a volume of cm3, a height of 3 cm, and an unknown radius . From the volume formula, we know:
Looking at the structure of the equation, we can see that , so the radius must be 8 cm.
Now imagine a different cone with a volume of cm3, a radius of 3 cm, and an unknown height . Using the formula for the volume of the cone, we know:
So, the height must be 6 cm. Can you see why?