8th Grade Math Worksheets | Free Downloads Available - Free Printable

Let's solve each problem step by step using the appropriate volume formulas.

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Volume Formulas:

- Pyramid:
$$
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
$$

- Cone:
$$
V = \frac{1}{3} \pi r^2 h
$$

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

> Note: There are no spheres in this worksheet, only pyramids and cones.

We'll calculate each one:

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1) Square Pyramid

- Base: 4 cm × 4 cm → Area = $4 \times 4 = 16\,\text{cm}^2$
- Height = 9 cm
$$
V = \frac{1}{3} \times 16 \times 9 = \frac{144}{3} = 48\,\text{cm}^3
$$

✔ Volume = 48.00 cm³

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2) Rectangular Pyramid

- Base: 12 cm × 6 cm → Area = $12 \times 6 = 72\,\text{cm}^2$
- Height = 15 cm
$$
V = \frac{1}{3} \times 72 \times 15 = 24 \times 15 = 360\,\text{cm}^3
$$

✔ Volume = 360.00 cm³

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3) Rectangular Pyramid

- Base: 5 cm × 7 cm → Area = $5 \times 7 = 35\,\text{cm}^2$
- Height = 20 cm
$$
V = \frac{1}{3} \times 35 \times 20 = \frac{700}{3} \approx 233.33\,\text{cm}^3
$$

✔ Volume = 233.33 cm³

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4) Triangular Prism with a Pyramid on Top? Wait...

Wait — this shape looks like a rectangular prism with a pyramid on top, but actually, looking at the diagram: it’s a square pyramid sitting on top of a rectangular prism?

But the labels show:
- Base of the base rectangle: 3 cm × 2 cm
- Height from base to apex: 7 cm (vertical dashed line)
- The bottom part is a box-like shape with height 2 cm, width 3 cm, depth 3 cm? Wait, dimensions are:
- Bottom face: 3 cm × 3 cm?
- Side: 2 cm high
- Then a pyramid on top with height 7 cm?

But wait — the entire figure has a pyramid with a rectangular base of 3 cm × 3 cm, and height 7 cm?

Looking again:
The base is a rectangle: 3 cm × 3 cm? But labeled as 3 cm and 2 cm? No.

Wait:
- Bottom face: 3 cm × 2 cm → area = $3 \times 2 = 6\,\text{cm}^2$
- But the vertical edge is 2 cm → maybe the base is 3 cm × 3 cm?

Wait, the base is shown as a rectangle with sides 3 cm and 2 cm? But then the height of the pyramid is 7 cm.

Actually, the base is a rectangle: 3 cm × 3 cm? No — let's read carefully.

From the image:
- The base is 3 cm × 2 cm → so area = $3 \times 2 = 6\,\text{cm}^2$
- Height of pyramid = 7 cm

So:
$$
V = \frac{1}{3} \times 6 \times 7 = \frac{42}{3} = 14\,\text{cm}^3
$$

✔ Volume = 14.00 cm³

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5) Cone

- Radius = 3 cm
- Height = 9 cm
$$
V = \frac{1}{3} \pi r^2 h = \frac{1}{3} \pi (3)^2 (9) = \frac{1}{3} \pi \times 9 \times 9 = \frac{81}{3} \pi = 27\pi
$$
$$
27\pi \approx 27 \times 3.1416 = 84.82\,\text{cm}^3
$$

✔ Volume ≈ 84.82 cm³

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6) Cone

- Radius = 1.5 cm
- Height = 7 cm
$$
V = \frac{1}{3} \pi (1.5)^2 (7) = \frac{1}{3} \pi (2.25)(7) = \frac{1}{3} \pi \times 15.75 = 5.25\pi
$$
$$
5.25\pi \approx 5.25 \times 3.1416 \approx 16.49\,\text{cm}^3
$$

✔ Volume ≈ 16.49 cm³

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7) Cone

- Diameter = 20 cm → Radius = 10 cm
- Height = 24 cm
$$
V = \frac{1}{3} \pi (10)^2 (24) = \frac{1}{3} \pi \times 100 \times 24 = \frac{2400}{3} \pi = 800\pi
$$
$$
800\pi \approx 800 \times 3.1416 = 2513.27\,\text{cm}^3
$$

✔ Volume ≈ 2513.27 cm³

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8) Cone

- Diameter = 7.2 mm → Radius = $7.2 / 2 = 3.6$ mm
- Height = 7.7 mm
$$
V = \frac{1}{3} \pi (3.6)^2 (7.7)
$$
First: $3.6^2 = 12.96$

Then: $12.96 \times 7.7 = 100.032$

Then: $\frac{1}{3} \times 100.032 = 33.344$

Now: $33.344 \times \pi \approx 33.344 \times 3.1416 \approx 104.64\,\text{mm}^3$

✔ Volume ≈ 104.64 mm³

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✔ Final Answers:

| Problem | Volume |
|--------|--------|
| 1) | 48.00 cm³ |
| 2) | 360.00 cm³ |
| 3) | 233.33 cm³ |
| 4) | 14.00 cm³ |
| 5) | 84.82 cm³ |
| 6) | 16.49 cm³ |
| 7) | 2513.27 cm³ |
| 8) | 104.64 mm³ |

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🔍 Explanation Summary:

- For pyramids, use: $ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} $
- For cones, use: $ V = \frac{1}{3} \pi r^2 h $
- Always ensure units match.
- Use $ \pi \approx 3.1416 $ for calculations.
- Round to 2 decimal places where needed.

Let me know if you'd like these written out neatly for printing or submission!