Volume of a Prism Worksheets - Free Printable

Let's solve each of the 9 volume problems step by step. We'll use standard volume formulas for each shape:

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1) Cylinder

- Radius (r) = 3 m
- Height (h) = 7 m
Volume of a cylinder:
$$
V = \pi r^2 h = \pi (3)^2 (7) = \pi \cdot 9 \cdot 7 = 63\pi \, \text{m}^3
$$
✔ Answer: $63\pi$ m³

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2) Triangular Prism

- Base of triangle = 13 ft
- Height of triangle = 11 ft
- Length (depth) of prism = 15 ft
Volume of triangular prism:
$$
V = \text{Base Area} \times \text{Length} = \left(\frac{1}{2} \cdot 13 \cdot 11\right) \cdot 15 = (71.5) \cdot 15 = 1072.5 \, \text{ft}^3
$$
✔ Answer: 1072.5 ft³

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3) Sphere

- Radius (r) = 3 m
Volume of a sphere:
$$
V = \frac{4}{3} \pi r^3 = \frac{4}{3} \pi (3)^3 = \frac{4}{3} \pi \cdot 27 = 36\pi \, \text{m}^3
$$
✔ Answer: $36\pi$ m³

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4) Rectangular Prism (Cuboid)

- Length = 12 mm
- Width = 8 mm
- Height = 4 mm
Volume:
$$
V = l \cdot w \cdot h = 12 \cdot 8 \cdot 4 = 384 \, \text{mm}^3
$$
✔ Answer: 384 mm³

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5) Cone

- Radius (r) = 3 m
- Height (h) = 7 m
Volume of a cone:
$$
V = \frac{1}{3} \pi r^2 h = \frac{1}{3} \pi (3)^2 (7) = \frac{1}{3} \pi \cdot 9 \cdot 7 = 21\pi \, \text{m}^3
$$
✔ Answer: $21\pi$ m³

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6) Cylinder

- Diameter = 10 cm → Radius = 5 cm
- Height = 11 cm
Volume:
$$
V = \pi r^2 h = \pi (5)^2 (11) = \pi \cdot 25 \cdot 11 = 275\pi \, \text{cm}^3
$$
✔ Answer: $275\pi$ cm³

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7) Parallelepiped (Slanted Prism with Triangle Base?) Wait – Actually, it's a Prism with Trapezoidal Base?** Let’s analyze.

Wait — looking at the figure: It's a parallelogram-shaped base, but the side shows a right triangle with legs 9 cm and 12 cm, and the base is 18 cm.

Actually, this is a prism with a parallelogram base, but we can treat it as a rectangular prism if the cross-section is uniform.

But wait: The figure shows a slanted top, but with a perpendicular height of 9 cm, and the base is 18 cm long, and the side is 12 cm. But actually, the height of the parallelogram is given as 9 cm, and the base is 18 cm.

So, base area = base × height = $18 \cdot 9 = 162$ cm²

Then the depth of the prism (length) is 12 cm? Wait — no.

Wait: The side labeled "12 cm" has a right angle, so it's the height of the prism? Let’s re-analyze.

Actually, from the diagram:
- The base of the parallelogram is 18 cm.
- The height of the parallelogram is 9 cm (perpendicular).
- The depth (length) of the prism is 12 cm (since the side is 12 cm and marked with a right angle).

Wait — the figure looks like a parallelepiped where the base is a parallelogram with base 18 cm and height 9 cm, and the depth is 12 cm.

So:
- Base area = $18 \cdot 9 = 162$ cm²
- Height of prism = 12 cm
- Volume = Base Area × Height = $162 \cdot 12 = 1944$ cm³

✔ Answer: 1944 cm³

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8) Rectangular Prism

- Length = 10 ft
- Width = 6 ft
- Height = 6 ft
Volume:
$$
V = 10 \cdot 6 \cdot 6 = 360 \, \text{ft}^3
$$
✔ Answer: 360 ft³

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9) Rectangular Prism

- Length = 11 in
- Width = 4 in
- Height = 14 in
Volume:
$$
V = 11 \cdot 4 \cdot 14 = 616 \, \text{in}^3
$$
✔ Answer: 616 in³

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✔ Final Answers Summary:

| Problem | Shape | Volume |
|--------|------------------|----------------------------|
| 1 | Cylinder | $63\pi$ m³ |
| 2 | Triangular Prism | 1072.5 ft³ |
| 3 | Sphere | $36\pi$ m³ |
| 4 | Rectangular Prism| 384 mm³ |
| 5 | Cone | $21\pi$ m³ |
| 6 | Cylinder | $275\pi$ cm³ |
| 7 | Prism (Parallelogram Base) | 1944 cm³ |
| 8 | Rectangular Prism| 360 ft³ |
| 9 | Rectangular Prism| 616 in³ |

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🔍 Explanation Recap:

- Cylinder: $ V = \pi r^2 h $
- Triangular Prism: $ V = \frac{1}{2} \cdot b \cdot h_{\text{triangle}} \cdot L $
- Sphere: $ V = \frac{4}{3} \pi r^3 $
- Rectangular Prism: $ V = l \cdot w \cdot h $
- Cone: $ V = \frac{1}{3} \pi r^2 h $
- Prism with parallelogram base: $ V = (\text{base area}) \times \text{height} $

Let me know if you'd like these answers formatted for printing or want decimal approximations (e.g., using $\pi \approx 3.14$).