What you’ll learn
Calculate cone volume.
Key idea
Cone volume is one third of circular base area times perpendicular height.
Cone volume is one third of its matching cylinder; slant is not height.
Worked example
Enter the exact value or ordered values in the format requested below.
A right circular cone has diameter 4 cm and perpendicular height 9 cm. Find exact volume in cubic cm as a multiple of pi, without a unit suffix.
- The radius is 2, so base area=4π.
- Volume=4π*9/3=12π cubic cm.
Answer: 12π
Quick Check
Evaluate a worked attempt at calculate cone volume, identify the first invalid step, and provide the correction.
A cone has radius 3 and perpendicular height 11. Step 1 correctly gets base area 9π from radius 3. Step 2 gives volume 99π by multiplying without one third. Locate and repair the first invalid step.