What you’ll learn
Calculate sphere volume.
Key idea
Sphere volume uses four thirds times pi times radius cubed, not squared.
Volume scales with radius cubed; take a positive cube root before deriving a diameter.
Worked example
Enter the exact value or ordered values in the format requested below.
A sphere has diameter 18 cm. Find its exact volume in cubic cm as a multiple of pi, without a unit suffix.
- True radius=9, so its cube is 729.
- Volume=(4/3)*pi*729=972π cubic cm.
Answer: 972π
Quick Check
Evaluate a worked attempt at calculate sphere volume, identify the first invalid step, and provide the correction.
A sphere has radius 11. Step 1 normalizes radius to 11 but uses V=(4/3)*pi*radius^2. Step 2 obtains (484/3)π. Locate and repair the first invalid step.