What you’ll learn
Calculate cone volume.
Key idea
A cone has one third the volume of a cylinder with matching circular base and perpendicular height.
Matching-cylinder volume must be divided by three; slant length cannot replace perpendicular height.
Worked example
Enter the exact value or ordered values in the format requested below.
Right circular cone radius 3 cm,perpendicular height 18 cm. Enter exact pi-volume with cm³ understood; omit unit.
- Matching cylinder coefficient is 3²×18=162.
- Cone volume takes one third: 54π cm³; reversing gives height=3×54/9=18 cm.
Answer: 54π
Quick Check
Evaluate a worked attempt at calculate cone volume, identify the first invalid step, and provide the correction.
Cone radius 6 cm,height 3 cm: Step 1 finds matching cylinder volume 108π cm³. Step 2 calls that the cone volume without adjustment. Locate the first invalid step and correct it.