Volume of Spheres - SCAFFOLDED WORKSHEET - Free Printable

Let’s solve each sphere volume problem step by step using the formula:

V = (4/3)πr³

We’ll calculate each one carefully, rounding to one decimal place at the end.

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🟡 Sphere 1: Radius = 5 in

V = (4/3) × π × 5³
5³ = 125
V = (4/3) × π × 125 = (500/3)π ≈ 166.666...π
Now multiply by π ≈ 3.1416 → 166.666... × 3.1416 ≈ 523.6

✔ Final: 523.6 in³

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🟢 Sphere 2: Radius = 7 ft

V = (4/3) × π × 7³
7³ = 343
V = (4/3) × π × 343 = (1372/3)π ≈ 457.333...π
× π ≈ 457.333 × 3.1416 ≈ 1436.8

✔ Final: 1436.8 ft³

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🟣 Sphere 3: Radius = 3 cm

V = (4/3) × π × 3³
3³ = 27
V = (4/3) × π × 27 = 36π
× π? Wait — no! The formula already has π in it. So we compute numerically:

Actually, let’s clarify: In the worksheet, they write “V = ___ π” first, then “V = _____ unit³”. So for this one:

First line: V = (4/3) × π × 3³ → so fill in blanks:
→ V = 4/3 × π × 27
Then simplify: (4/3)*27 = 36 → so V = 36π
Then numerical value: 36 × 3.1416 ≈ 113.1

✔ Final: 113.1 cm³

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🟠 Sphere 4: Diameter = 12 yd → Radius = 6 yd

V = (4/3) × π × 6³
6³ = 216
V = (4/3) × π × 216 = (864/3)π = 288π
Numerical: 288 × 3.1416 ≈ 904.8

✔ Final: 904.8 yd³

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🔵 Sphere 5: Diameter = 18 mm → Radius = 9 mm

V = (4/3) × π × 9³
9³ = 729
V = (4/3) × π × 729 = (2916/3)π = 972π
Numerical: 972 × 3.1416 ≈ 3053.6

✔ Final: 3053.6 mm³

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🔴 Sphere 6: Diameter = 28 m → Radius = 14 m

V = (4/3) × π × 14³
14³ = 2744
V = (4/3) × π × 2744 = (10976/3)π ≈ 3658.666...π
Numerical: 3658.666... × 3.1416 ≈ 11494.0

Wait — let me double-check that multiplication:

3658.666... × 3.1416

Break it down:

3658.666 × 3 = 10976
3658.666 × 0.1416 ≈ ?

First, 3658.666 × 0.1 = 365.8666
3658.666 × 0.04 = 146.34664
3658.666 × 0.0016 = ~5.8538656
Add them: 365.8666 + 146.34664 = 512.21324 + 5.8538656 ≈ 518.067

Total: 10976 + 518.067 ≈ 11494.067

Rounded to one decimal: 11494.1

But wait — let me use calculator-style precision:

(4/3) * π * 14^3 = (4/3)*π*2744 = (10976/3)*π = 3658.666666... * π

π ≈ 3.1415926535

3658.666666 * 3.1415926535 ≈ ?

Let me compute:

3658.666666 × 3.1415926535

Use approximation:

≈ 3658.6667 × 3.1416 ≈ as above ~11494.067 → rounds to 11494.1

But let me check with exact fraction:

V = (4/3)πr³ = (4/3)π(2744) = (10976/3)π

10976 ÷ 3 = 3658.666...

3658.666... × 3.141592653589793 =

Let me do precise calc:

3658.6666666666665 × 3.141592653589793 =

Using calculator input: 10976 / 3 * pi =

In Python style: (10976/3)*math.pi → approximately 11494.0403...

So actually ≈ 11494.0 when rounded to one decimal? Wait:

11494.0403 → tenths place is 0, hundredths is 4 → so round down → 11494.0

Wait — I think I made a mistake earlier.

Let me recalculate all with consistent precision.

Actually, better to use:

For Sphere 6: r = 14

V = (4/3) * π * 14^3 = (4/3)*π*2744 = (10976/3)π

Compute 10976 ÷ 3 = 3658.666666...

Now 3658.666666... × π

π = 3.141592653589793

Multiply:

3658.6666666666665 × 3.141592653589793 =

Let me compute step by step:

First, 3658.6666666666665 × 3 = 10976

Then 3658.6666666666665 × 0.141592653589793

Compute 3658.6666666666665 × 0.14 = 512.2133333333333

3658.6666666666665 × 0.001592653589793 ≈ ?

3658.6666666666665 × 0.001 = 3.6586666666666665

3658.6666666666665 × 0.0005 = 1.8293333333333332

3658.6666666666665 × 0.000092653589793 ≈ 3658.6667 × 0.00009265 ≈ 0.339

Better: 3658.6667 × 0.000092653589793 ≈ let's say approx 0.339

So total for 0.00159265... part: 3.6587 + 1.8293 + 0.339 ≈ 5.827

So total extra: 512.2133 + 5.827 ≈ 518.0403

Thus total V ≈ 10976 + 518.0403 = 11494.0403

So to one decimal place: look at hundredths digit → 4, which is less than 5 → so 11494.0

Yes.

✔ Final: 11494.0 m³

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Now let’s compile all answers clearly.

Also note: For Sphere 3, they have blanks:

“V = __ × __ × __³” → should be 4/3, π, and 3 (since radius is 3)

And “V = ___ π” → 36π

Then “V = _____ cm³” → 113.1

Similarly for others.

But since the user just wants the final volumes filled in the last blank of each box, we provide those.

Final Answers per sphere:

1. Yellow: 523.6 in³
2. Green: 1436.8 ft³
3. Purple: 113.1 cm³
4. Orange: 904.8 yd³
5. Blue: 3053.6 mm³
6. Pink: 11494.0 m³

All rounded to one decimal place.

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Final Answer:
Yellow sphere: 523.6 in³
Green sphere: 1436.8 ft³
Purple sphere: 113.1 cm³
Orange sphere: 904.8 yd³
Blue sphere: 3053.6 mm³
Pink sphere: 11494.0 m³