What you’ll learn
Calculate sphere volume.
Key idea
Sphere volume uses four thirds times pi times radius cubed; the input must be the radius.
Use radius cubed with four-thirds; halve diameter before substitution and retain cubic units.
Worked example
Enter the exact value or ordered values in the format requested below.
Sphere radius 3 cm. Enter exact pi-volume with cm³ understood; omit unit and do not approximate pi.
- Radius 3 cm is half diameter 6 cm; radius cube=27.
- Sphere volume=(4/3)π×27=36π cm³; inverse radius cube=(3/4)×36=27, whose positive cube root is 3 cm.
Answer: 36π
Quick Check
Evaluate a worked attempt at calculate sphere volume, identify the first invalid step, and provide the correction.
Sphere diameter 28 cm: Step 1 uses 28 as radius. Step 2 applies (4/3)πr³ to obtain (87808/3)π cm³. Identify the first invalid step and correct the volume.