Volume of a Sphere - Worksheets - Free Printable

Let's solve each problem step by step using the volume formula for a sphere:

$$
V = \frac{4}{3} \pi r^3
$$

We are told to use $ \pi \approx 3.14 $, and round answers to the nearest tenth.

---

Problem 1: Radius = 2 m

$$
V = \frac{4}{3} \times 3.14 \times (2)^3
= \frac{4}{3} \times 3.14 \times 8
= \frac{4}{3} \times 25.12
= 33.493\ldots
$$

Rounded to the nearest tenth:
✔ 33.5 cm³

> Note: The unit is given as "m" (meters), but the answer box says "cm³". That seems inconsistent. However, since the question asks for volume in cm³, we assume it’s a typo and proceed with the units as given. But let’s keep the unit consistent with input — if radius is in meters, volume will be in m³, unless converted.

But looking at the original example, they used cm. So likely, all measurements are in centimeters, even if labeled otherwise.

Wait — Problem 1 says 2 m, but others have mm or cm. Let’s check:

- 1. 2 m → probably a typo? Or maybe not. But since the final answer is expected in cm³, we must convert.

But the problem says: "Find the volume of each sphere. Use 3.14 for π. Round your answer to the nearest tenth."

It doesn't specify units for the answer, but based on the example (cm³), and the image shows cm in the first example, we should assume that all radii are in centimeters, even if some are labeled differently.

Wait — let’s look again:

- 1. 2 m → but the diagram has a red line labeled "2 m"
- 2. 5 cm
- 3. 10 mm
- 4. 3 mm
- 5. 8 m
- 6. 7 cm

This is inconsistent. But likely, the labels are meant to be in centimeters, or we need to convert.

But since the example uses cm, and the worksheet is likely designed for consistent units, perhaps the "m" and "mm" are typos?

Alternatively, maybe the units are correct, and we need to compute accordingly.

Let’s go one by one, using the unit as written, and convert to cm if needed for consistency.

But volume units depend on the input unit.

Let’s clarify:

- If radius is in meters, volume is in m³
- If radius is in millimeters, volume is in mm³
- But the example uses cm³, so perhaps all inputs should be converted to cm?

Wait — the example shows a radius of 4 cm, and volume in cm³.

So likely, all radii are in centimeters, and the labels like "2 m" might be mistakes.

But let’s double-check the image:

Looking at the image:

- Problem 1: radius labeled "2 m" → this is suspicious.
- Problem 2: "5 cm" → good
- Problem 3: "10 mm" → millimeters
- Problem 4: "3 mm"
- Problem 5: "8 m"
- Problem 6: "7 cm"

This suggests inconsistent units.

But since the example uses cm, and the answer is in cm³, likely the intention is to convert all to centimeters before calculating.

Let’s do that.

---

Step-by-step solutions:

---

1. Radius = 2 m

Convert to cm:
2 m = 200 cm

$$
V = \frac{4}{3} \times 3.14 \times (200)^3
= \frac{4}{3} \times 3.14 \times 8,000,000
= \frac{4}{3} \times 25,120,000
= 33,493,333.33...
$$

→ ≈ 33,493,333.3 cm³

But this is huge — probably not intended.

Alternatively, maybe the "m" is a typo, and it should be cm.

Similarly, "8 m" in problem 5 is also large.

Let’s assume all radii are in centimeters, and the labels like "m" or "mm" are typos.

Because otherwise, volumes would be enormous or tiny.

Alternatively, perhaps the labels are correct, and we should use them as-is.

Let’s try another interpretation.

Maybe the units are just labels, and the numbers are what matter.

But let’s look at problem 3: radius = 10 mm

Then:
10 mm = 1 cm

So volume would be small.

But problem 1: 2 m = 200 cm → very large

But the example had 4 cm → ~267 cm³

So if problem 1 has 2 cm instead of 2 m, it would make sense.

So likely, the units are mislabeled.

Let’s assume the following:

- All radii are in centimeters, regardless of label.
- Or, more precisely, the numbers are correct, and the units are typos.

But to be safe, let’s assume the radius values are in centimeters, and ignore the unit labels (or interpret them as cm).

Alternatively, perhaps:

- 1. 2 cm (not m)
- 2. 5 cm
- 3. 10 mm = 1 cm
- 4. 3 mm = 0.3 cm
- 5. 8 m = 800 cm → too big
- 6. 7 cm

Still inconsistent.

Another idea: Maybe the labels are correct, and we must convert to cm.

Let’s do it properly.

---

Let's re-evaluate with correct unit conversions.

We’ll convert all radii to centimeters, then compute volume in cm³.

---

#### 1. Radius = 2 m

2 m = 200 cm

$$
V = \frac{4}{3} \times 3.14 \times (200)^3
= \frac{4}{3} \times 3.14 \times 8,000,000
= \frac{4}{3} \times 25,120,000 = 33,493,333.33...
$$

≈ 33,493,333.3 cm³

That’s 33.5 million cm³ — seems unreasonable for a worksheet.

---

#### 2. Radius = 5 cm

$$
V = \frac{4}{3} \times 3.14 \times (5)^3
= \frac{4}{3} \times 3.14 \times 125
= \frac{4}{3} \times 392.5 = 523.333...
$$

≈ 523.3 cm³

OK.

---

#### 3. Radius = 10 mm

10 mm = 1 cm

$$
V = \frac{4}{3} \times 3.14 \times (1)^3 = \frac{4}{3} \times 3.14 = 4.1867...
$$

≈ 4.2 cm³

OK.

---

#### 4. Radius = 3 mm

3 mm = 0.3 cm

$$
V = \frac{4}{3} \times 3.14 \times (0.3)^3
= \frac{4}{3} \times 3.14 \times 0.027
= \frac{4}{3} \times 0.08478 = 0.11304
$$

≈ 0.1 cm³

OK.

---

#### 5. Radius = 8 m

8 m = 800 cm

$$
V = \frac{4}{3} \times 3.14 \times (800)^3
= \frac{4}{3} \times 3.14 \times 512,000,000
= \frac{4}{3} \times 1,607,680,000 = 2,143,573,333.33...
$$

≈ 2,143,573,333.3 cm³ → about 2.1 billion cm³

Too big.

---

#### 6. Radius = 7 cm

$$
V = \frac{4}{3} \times 3.14 \times (7)^3
= \frac{4}{3} \times 3.14 \times 343
= \frac{4}{3} \times 1,077.02 = 1,436.0267
$$

≈ 1,436.0 cm³

OK.

---

Given that problems 1 and 5 give extremely large volumes, and the example is only ~267 cm³, it’s very likely that the unit labels are typos, and all radii are meant to be in centimeters.

So let’s assume:

- 1. 2 cm (not m)
- 2. 5 cm
- 3. 10 mm → 1 cm
- 4. 3 mm → 0.3 cm
- 5. 8 cm (not m)
- 6. 7 cm

And compute accordingly.

Let’s go with that.

---

✔ Corrected Assumption: All radii are in centimeters, except where noted.

But 3 and 4 are in mm, so convert to cm.

---

1. Radius = 2 cm

$$
V = \frac{4}{3} \times 3.14 \times (2)^3
= \frac{4}{3} \times 3.14 \times 8
= \frac{4}{3} \times 25.12 = 33.493...
$$

≈ 33.5 cm³

---

2. Radius = 5 cm

$$
V = \frac{4}{3} \times 3.14 \times 125 = \frac{4}{3} \times 392.5 = 523.333...
$$

≈ 523.3 cm³

---

3. Radius = 10 mm = 1 cm

$$
V = \frac{4}{3} \times 3.14 \times (1)^3 = \frac{4}{3} \times 3.14 = 4.1867...
$$

≈ 4.2 cm³

---

4. Radius = 3 mm = 0.3 cm

$$
V = \frac{4}{3} \times 3.14 \times (0.3)^3
= \frac{4}{3} \times 3.14 \times 0.027
= \frac{4}{3} \times 0.08478 = 0.11304
$$

≈ 0.1 cm³

---

5. Radius = 8 cm (assuming "8 m" is typo)

$$
V = \frac{4}{3} \times 3.14 \times (8)^3
= \frac{4}{3} \times 3.14 \times 512
= \frac{4}{3} \times 1,607.68 = 2,143.573...
$$

≈ 2,143.6 cm³

---

6. Radius = 7 cm

$$
V = \frac{4}{3} \times 3.14 \times (7)^3
= \frac{4}{3} \times 3.14 \times 343
= \frac{4}{3} \times 1,077.02 = 1,436.0267
$$

≈ 1,436.0 cm³

---

Final Answers (rounded to nearest tenth):

| Problem | Radius | Volume (cm³) |
|--------|--------|--------------|
| 1 | 2 cm | 33.5 |
| 2 | 5 cm | 523.3 |
| 3 | 1 cm | 4.2 |
| 4 | 0.3 cm | 0.1 |
| 5 | 8 cm | 2,143.6 |
| 6 | 7 cm | 1,436.0 |

---

✔ Summary:

Even though the labels show mixed units, the most reasonable interpretation is that the radii are meant to be in centimeters, or the units are typos.

Therefore, the volumes are:

1. 33.5 cm³
2. 523.3 cm³
3. 4.2 cm³
4. 0.1 cm³
5. 2,143.6 cm³
6. 1,436.0 cm³

---

If you believe the original units are correct, then the volumes would be much larger (e.g., 33 million cm³ for #1), but that seems unlikely for a classroom worksheet.

Thus, we conclude the units are likely typos, and the radii are in centimeters.

Let me know if you'd like the answers formatted for submission!