Sphere volumeRadius or diameter
Name: Date:
Find the volume of each sphere. Use π = 3.14. Round to the hundredth.
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Volume of a sphere worksheets
The volume of a sphere is four-thirds π r cubed, and almost every mark lost on it is lost before that formula is reached. These free printable worksheets label some figures with a radius and some with a diameter, so the first step is always reading which one you were given.
Kid stuck on one? You don’t just get the sheet.
Volume of a sphere
The answer key prints on a separate page.
What's on this sheet
Halving a diameter is one keystroke and it is the step that disappears under pressure. A sphere 18 cm across has a radius of 9, and using 18 gives an answer eight times too big — a mistake large enough that a rough estimate would catch it, which is exactly why estimating first is worth the ten seconds.
Why this sheet works
Cubing is the other half. r³ means r × r × r, not r × 3, and the two are only equal when r is nothing useful. Working the cube out on its own line before multiplying by four-thirds keeps the two operations from colliding.
How this one works
One question from this sheet, worked through a step at a time.
Volume of a sphere, radius 10 cm
radius: 10 cm
10 × 10 × 10=1000
4/3 × 3.14 ×1000≈4186.67
4186.67 cm³
- The 10 cm marked here runs from the center to the surface, so it is already the radius — which is what the formula wants.
- Cube the radius on a line of its own. r³ means r × r × r, not r × 3: 10 × 10 × 10 = 1000.
- Then four-thirds of that, times π: 4/3 × 3.14 × 1000 comes to 4186.6667…, which is 4186.67 to two decimal places. A third rarely lands on a whole number of hundredths, so this kind of answer is usually rounded.
- So the volume is 4186.67 cubic cm. Cubic, not square — a volume fills a space, and the unit is the quickest way to notice you have answered a surface-area question instead.