Volume of Spheres - SCAFFOLDED WORKSHEET - Free Printable

Let’s solve each sphere volume problem step by step.

We use the formula:
V = (4/3) × π × r³

Remember:
- If you’re given radius, plug it in directly.
- If you’re given diameter, divide by 2 to get radius first.
- Always cube the radius (r³ = r × r × r).
- Multiply by 4/3 and then by π.
- Round final answer to one decimal place.

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🟡 Sphere 1: Radius = 5 in

V = (4/3) × π × 5³
5³ = 5 × 5 × 5 = 125
V = (4/3) × π × 125 = (500/3)π ≈ 166.666...π
Now multiply by π? Wait — no! The worksheet shows “V = ___ π” first, then “V = ____ in³”. So we leave it as multiple of π first, then compute numerical value.

Actually, looking at the blanks:

First blank after “× __³” → that’s the radius cubed → 125
Then “V = ___ π” → that’s (4/3)*125 = 500/3 ≈ 166.7 (but they want exact fraction times π?)
Wait — let’s check the structure:

It says:
V = 4/3 × π × ___³ → fill in radius → 5
Then V = ___ π → this is (4/3)*r³ → so (4/3)*125 = 500/3 → but maybe they want decimal? No, probably keep as fraction or rounded? But next line is “V = _____ in³” which is numerical.

Looking at other problems, for example purple one:
“V = _ × _ × _³” — that seems to be filling in 4/3, π, and r³ separately? Let me re-read.

Actually, looking carefully:

For yellow sphere:
V = 4/3 × π × ___³ → fill in 5
Then V = ___ π → this should be (4/3)*5³ = (4/3)*125 = 500/3 → but 500/3 is about 166.666..., so perhaps write 166.7? But it says “___ π”, meaning coefficient of π.

But then next line: V = ______ in³ → that’s the actual number, so multiply by π.

I think the intention is:

Line 1: Fill in radius → 5
Line 2: Compute (4/3)*r³ → so 500/3 → but since it says “___ π”, maybe they want the coefficient as a decimal? Or fraction? Looking at green sphere same thing.

Wait — perhaps better to compute numerically from start.

Standard way: Compute V = (4/3)πr³, then round to one decimal.

But the worksheet has intermediate steps.

Let me interpret based on common teaching practice:

For yellow sphere (r=5):

V = 4/3 × π × 5³ → fill 5 in blank
Then V = (4/3 * 125) π = 500/3 π → so write 500/3 or 166.7? Since next step is numerical, probably they want 166.7 here? But 500/3 is exact.

Looking at purple sphere: it says “V = _ × _ × _³” — that might be for 4/3, π, and r³.

Ah! I see now.

In purple sphere:
V = _ × _ × _³ → likely: 4/3 × π × 3³

Similarly, for others.

So let’s do each one properly.

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## 🔵 Yellow Sphere: radius = 5 in

Step 1: V = (4/3) × π × r³ = (4/3) × π × 5³
Fill first blank: 5

Step 2: Compute (4/3) × 5³ = (4/3) × 125 = 500/3 ≈ 166.666...
So V = 166.7 π ? But that doesn’t make sense because π is still there. Actually, no — the expression is V = [coefficient] π, so coefficient is 500/3.

But 500/3 is approximately 166.666..., so if we write to one decimal, it’s 166.7? But typically we don’t round until final answer.

Perhaps they want exact fraction? But instruction says “give your answer to one decimal place” for final volume.

Looking at the lines:

After “V = ___ π”, then “V = ______ in³”

So probably:

- First blank after × __³ : radius → 5
- Then V = ___ π : this is (4/3)r³ → 500/3 → but since it's followed by numerical, maybe they expect us to compute (4/3)r³ as decimal? 166.7?
- Then V = ______ in³ : multiply by π → 166.666... × π ≈ 523.6

Let me calculate numerically:

V = (4/3) * π * 125 = (500/3) * π ≈ 166.6667 * 3.1416 ≈ let's compute:

166.6667 * 3.1416 ≈ ?

First, 166.6667 * 3 = 500
166.6667 * 0.1416 ≈ 166.6667 * 0.14 = 23.3333, plus 166.6667 * 0.0016 ≈ 0.2667, total ≈ 23.6
So total ≈ 500 + 23.6 = 523.6

Yes, standard value: volume of sphere r=5 is (4/3)π(125) = 500π/3 ≈ 523.598... → rounds to 523.6 in³

But for the intermediate "V = ___ π", what to put? 500/3 or 166.7?

Since the next part is numerical, and they say "to one decimal place" for final answer, probably for "V = ___ π" they want the coefficient as a decimal rounded to one decimal? 166.7

Similarly for others.

Let me confirm with another one.

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## 🟢 Green Sphere: radius = 7 ft

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

So V = 457.3 π ? Then numerical: 457.333 * π ≈ 457.333 * 3.1416 ≈ let's compute:

457.333 * 3 = 1372
457.333 * 0.1416 ≈ 457.333 * 0.14 = 64.0266, plus 457.333 * 0.0016 ≈ 0.7317, total ≈ 64.7583
So total ≈ 1372 + 64.7583 = 1436.7583 → rounds to 1436.8 ft³

Standard calculation: (4/3)π(343) = 1372π/3 ≈ 1436.755 → yes, 1436.8

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## 🟣 Purple Sphere: radius = 3 cm

Here it says: V = _ × _ × _³

Probably: 4/3 × π × 3³

So fill: 4/3, π, 3

Then V = ___ π → (4/3)*27 = 36 → so 36π

Then V = ______ cm³ → 36 * π ≈ 36 * 3.1416 = 113.0976 → rounds to 113.1 cm³

Note: 3³=27, (4/3)*27=36, yes.

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## 🟠 Orange Sphere: diameter = 12 yd → so radius = 6 yd

V = (4/3) × π × 6³
6³ = 216
(4/3)*216 = 288
So V = 288 π
Numerical: 288 * π ≈ 288 * 3.1416 = let's compute:

288 * 3 = 864
288 * 0.1416 = 288 * 0.14 = 40.32, plus 288 * 0.0016 = 0.4608, total 40.7808
Sum: 864 + 40.7808 = 904.7808 → rounds to 904.8 yd³

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## 🔵 Blue Sphere: diameter = 18 mm → radius = 9 mm

V = (4/3) × π × 9³
9³ = 729
(4/3)*729 = 4 * 243 = 972 (since 729 / 3 = 243)
So V = 972 π
Numerical: 972 * π ≈ 972 * 3.1416

Compute:
972 * 3 = 2916
972 * 0.1416 = 972 * 0.14 = 136.08, plus 972 * 0.0016 = 1.5552, total 137.6352
Sum: 2916 + 137.6352 = 3053.6352 → rounds to 3053.6 mm³

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## 🔴 Pink Sphere: diameter = 28 m → radius = 14 m

V = (4/3) × π × 14³
14³ = 14*14=196, 196*14=2744
(4/3)*2744 = (4 * 2744) / 3 = 10976 / 3 ≈ 3658.666...

So V = 3658.7 π ? (rounded to one decimal)

Numerical: 3658.666... * π ≈ ?

First, 10976 / 3 * π = (10976 π)/3

Compute numerically: 10976 * 3.1416 / 3

First, 10976 / 3 = 3658.666...

3658.666 * 3.1416

Or better: 10976 * π / 3

π ≈ 3.1415926535

10976 * 3.1415926535 = let's approximate:

10000 * 3.1415926535 = 31415.926535
976 * 3.1415926535 ≈ 976 * 3.1416 ≈ 976*3 = 2928, 976*0.1416≈138.2016, total ≈ 3066.2016
Sum ≈ 31415.926535 + 3066.2016 = 34482.128135

Divide by 3: 34482.128135 / 3 ≈ 11494.0427 → rounds to 11494.0 m³? Wait, that can't be right because earlier calculations were smaller.

Mistake: 14³ is 2744, yes. (4/3)*2744 = 10976/3 ≈ 3658.6667

3658.6667 * π ≈ 3658.6667 * 3.1416

Calculate:

3658.6667 * 3 = 10976
3658.6667 * 0.1416 = ?

First, 3658.6667 * 0.14 = 512.213338
3658.6667 * 0.0016 = 5.85386672
Sum ≈ 518.0672

Total V ≈ 10976 + 518.0672 = 11494.0672 → yes, approximately 11494.1 m³? But let's use calculator-style.

Standard value: V = (4/3)πr³ = (4/3)π(2744) = (10976/3)π

10976 ÷ 3 = 3658.666666...

3658.666666 * π = 3658.666666 * 3.1415926535 ≈

Use: 3658.666666 * 3.1415926535

Or recognize that 14^3 = 2744, 4/3 * 2744 = 10976/3

10976/3 * π = (10976 π)/3

Compute 10976 * 3.1415926535 = 34482.128 (as before)

34482.128 / 3 = 11494.042666... → so to one decimal place: 11494.0 m³? But 11494.0427 rounds to 11494.0? No, 0.0427 is less than 0.05, so yes, 11494.0

But typically we write without trailing zero? But instruction says one decimal place, so 11494.0

But let me confirm with known formula: for r=14, V= (4/3)π(2744) = 11494.040... yes, so 11494.0 when rounded to one decimal? 11494.040 is 11494.0 to one decimal? No!

Rounding to one decimal place means one digit after decimal.

11494.040 — the digit after decimal is 0, and next is 4, which is less than 5, so it remains 11494.0

But usually for such large numbers, we might expect more precision, but according to calculation, it's correct.

I recall that volume of sphere with r=14 is approximately 11494.04, so to one decimal place, it's 11494.0

But let's double-check the multiplication.

r=14, r³=2744

4/3 * 2744 = 4 * 914.666... no, 2744 / 3 = 914.666..., times 4 = 3658.666...

3658.666... * π

π = 3.141592653589793

3658.6666666666665 * 3.141592653589793 = let's compute step by step.

First, 3658.6666666666665 * 3 = 10976

3658.6666666666665 * 0.141592653589793

Compute 3658.6666666666665 * 0.14 = 512.2133333333333

3658.6666666666665 * 0.001592653589793 ≈ 3658.6667 * 0.00159265 ≈ ?

3658.6667 * 0.001 = 3.6586667

3658.6667 * 0.0005 = 1.82933335

3658.6667 * 0.00009265 ≈ 3658.6667 * 0.00009 = 0.32928, plus 3658.6667 * 0.00000265 ≈ 0.0097, total approx 0.33898

So total for 0.00159265 ≈ 3.6587 + 1.8293 + 0.3390 = 5.827

Better: 3658.6667 * 0.001592653589793

Calculate 3658.6667 * 1.592653589793 * 10^{-3}

First, 3658.6667 * 1.592653589793

Approximate: 3658.67 * 1.59265 ≈

3658.67 * 1.5 = 5488.005

3658.67 * 0.09265 ≈ 3658.67 * 0.09 = 329.2803, 3658.67 * 0.00265 ≈ 9.695, total 338.9753

Sum 5488.005 + 338.9753 = 5826.9803

Then * 10^{-3} = 5.8269803

So back to earlier: 3658.6667 * 0.141592653589793 = 3658.6667 * (0.14 + 0.001592653589793) = 512.213333 + 5.82698 ≈ 518.040313

Then total V = 10976 + 518.040313 = 11494.040313

So V ≈ 11494.0403 m³

To one decimal place: look at hundredths digit, which is 4, less than 5, so round down → 11494.0 m³

But typically, we might write it as 11494.0, but some might expect 11494.0, which is fine.

However, I recall that in many textbooks, for r=14, volume is often calculated as approximately 11494.0, so it's correct.

But let's list all answers.

Now, for the intermediate "V = ___ π", what to put?

For yellow: (4/3)*125 = 500/3 ≈ 166.666... → to one decimal? 166.7

Similarly for green: (4/3)*343 = 1372/3 ≈ 457.333... → 457.3

Purple: (4/3)*27 = 36 → exactly 36.0

Orange: (4/3)*216 = 288 → 288.0

Blue: (4/3)*729 = 972 → 972.0

Pink: (4/3)*2744 = 10976/3 ≈ 3658.666... → 3658.7

And for the "V = _ × _ × _³" in purple, it's likely 4/3, π, 3

Similarly, for others, but only purple has that format.

In the image, only purple sphere has "V = _ × _ × _³", others have "V = 4/3 × π × __³"

So for purple, fill: 4/3, π, 3

For others, just the radius in the blank.

Now, let's compile all answers.

Also, note units.

Final Answer section should have all filled values.

But the user didn't specify how to present, but since it's homework, probably list each sphere's answers.

But in Final Answer, perhaps summarize.

Since the task is to calculate, and provide final numerical volumes, but the worksheet has intermediates.

The instruction says: "Calculate the volume of each sphere below using the formula provided. Give your answer to one decimal place."

And "your answer" likely refers to the final numerical volume.

But the worksheet has blanks for intermediates too.

To be safe, I'll provide all required fills.

But for Final Answer, perhaps list the final volumes.

Looking at the response format, it says "Final Answer: [Provide only the final correct answer]"

But there are six spheres, so probably list all final volumes.

Perhaps in order.

Let me list for each sphere the final volume in cubic units, rounded to one decimal.

From above:

1. Yellow (r=5 in): 523.6 in³

2. Green (r=7 ft): 1436.8 ft³

3. Purple (r=3 cm): 113.1 cm³

4. Orange (d=12 yd, r=6 yd): 904.8 yd³

5. Blue (d=18 mm, r=9 mm): 3053.6 mm³

6. Pink (d=28 m, r=14 m): 11494.0 m³

For pink, 11494.0, but is it necessary to write .0? Since it's exactly to one decimal, yes.

Some might argue that 11494.0 is the same as 11494, but the instruction says "to one decimal place", so we include the .0.

Now, for the intermediates, but since the final answer is the volume, and the question is to calculate volume, I think the final numerical values are what matter.

But to be thorough, let's see what the worksheet expects.

In the purple sphere, it has "V = _ × _ × _³" which is different, so perhaps for that one, they want the factors.

But for consistency, I'll assume the main answer is the final volume.

Moreover, in the initial instruction, "calculate the volume", so final number.

So for Final Answer, I'll list the six volumes.

But how to present? Perhaps in a list.

Since it's a single box, maybe comma-separated or something.

I think best to state clearly.

Another thought: perhaps the "Final Answer" should be the completed worksheet values, but that might be messy.

Given the constraints, I'll provide the final numerical volumes for each sphere in order.

So:

Sphere 1 (yellow): 523.6 in³

Sphere 2 (green): 1436.8 ft³

Sphere 3 (purple): 113.1 cm³

Sphere 4 (orange): 904.8 yd³

Sphere 5 (blue): 3053.6 mm³

Sphere 6 (pink): 11494.0 m³

For pink, let me confirm the calculation once more.

r = 14 m

r³ = 14*14*14 = 196*14

196*10=1960, 196*4=784, total 2744, yes.

(4/3)*2744 = 4*2744 / 3 = 10976 / 3 = 3658.6666...

3658.6666 * π = 3658.6666 * 3.1415926535 ≈ as calculated 11494.0403, which rounds to 11494.0 when to one decimal place? 11494.0403 — the first decimal is 0, second is 4, so yes, 11494.0

But typically, rounding 11494.0403 to one decimal place: look at the tenths place, which is 0, and the hundredths is 4 < 5, so it remains 11494.0

Yes.

Some calculators might show 11494.0, so it's fine.

Now, for the answer.

I think that's all.

So Final Answer will be the list of volumes.

To match the format, perhaps write them in order.

Since the user might expect the filled blanks, but I think the primary request is the volume calculation.

Moreover, in the response, I can mention the intermediates in reasoning, but final answer is the volumes.

So I'll proceed.