Compare the volumes
When comparing a cone and a cylinder, use the volume formulas:
- Cylinder: (V=\pi r^2h)
- Cone: (V=\frac13\pi r^2h)
So, if a cone and a cylinder have the same radius and height, the cone’s volume is one-third of the cylinder’s volume.
Step-by-step method
- Find the radius and height of each solid.
- Compute each volume using the correct formula.
- Simplify the expressions completely.
- Compare the results by ratio, difference, or direct statement, depending on the question.
Helpful comparison idea
If both solids share the same (r) and (h), you can compare quickly:
[
V_{cone} : V_{cylinder} = 1 : 3
]
This means the cylinder holds three times as much as the cone.
Check your work
- Make sure the units are cubic units, such as (cm^3) or (m^3).
- Confirm that you used the cone factor (\frac13).
- If the answer is exact, keep (\pi) unless the problem asks for a decimal.
A good final check is to see whether the cone’s volume is less than the cylinder’s when the dimensions are the same.