Volume of a Pyramid Worksheets - Free Printable

Let's solve each pyramid volume problem step by step. The volume of a pyramid is given by the formula:

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

We will calculate the volume for each pyramid, rounding to two decimal places.

---

1)

- Base: Rectangle with dimensions 10 yd × 12 yd
- Height of pyramid: 17 yd

Base Area = $10 \times 12 = 120$ yd²
Volume = $\frac{1}{3} \times 120 \times 17 = 680.00$ yd³

✔ Volume = 680.00 yd³

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2)

- Base: Rectangle with dimensions 7 ft × 16 ft
- Height of pyramid: 19 ft

Base Area = $7 \times 16 = 112$ ft²
Volume = $\frac{1}{3} \times 112 \times 19 = \frac{2128}{3} \approx 709.33$ ft³

✔ Volume = 709.33 ft³

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3)

- Base: Triangle with base 10 in and height 15 in
- Height of pyramid: 11 in

Base Area = $\frac{1}{2} \times 10 \times 15 = 75$ in²
Volume = $\frac{1}{3} \times 75 \times 11 = 275.00$ in³

✔ Volume = 275.00 in³

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4)

- Base: Triangle with base 3 m and height 4 m
- Height of pyramid: 8 m

Base Area = $\frac{1}{2} \times 3 \times 4 = 6$ m²
Volume = $\frac{1}{3} \times 6 \times 8 = 16.00$ m³

✔ Volume = 16.00 m³

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5)

- Base: Square with side 7 yd
- Height of pyramid: 10 yd

Base Area = $7 \times 7 = 49$ yd²
Volume = $\frac{1}{3} \times 49 \times 10 = \frac{490}{3} \approx 163.33$ yd³

✔ Volume = 163.33 yd³

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6)

- Base: Rectangle with dimensions 13 ft × 8 ft
- Height of pyramid: 10 ft

Base Area = $13 \times 8 = 104$ ft²
Volume = $\frac{1}{3} \times 104 \times 10 = \frac{1040}{3} \approx 346.67$ ft³

✔ Volume = 346.67 ft³

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7)

- Base: Triangle with base 14 ft and height 8 ft
- Height of pyramid: 16 ft

Base Area = $\frac{1}{2} \times 14 \times 8 = 56$ ft²
Volume = $\frac{1}{3} \times 56 \times 16 = \frac{896}{3} \approx 298.67$ ft³

✔ Volume = 298.67 ft³

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8)

- Base: Rectangle with dimensions 11 in × 11 in (square)
- Height of pyramid: 18 in

Base Area = $11 \times 11 = 121$ in²
Volume = $\frac{1}{3} \times 121 \times 18 = \frac{2178}{3} = 726.00$ in³

✔ Volume = 726.00 in³

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9)

- Base: Rectangle with dimensions 15 yd × 8 yd
- Height of pyramid: 17 yd

Base Area = $15 \times 8 = 120$ yd²
Volume = $\frac{1}{3} \times 120 \times 17 = 680.00$ yd³

✔ Volume = 680.00 yd³

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✔ Final Answers:

| Problem | Volume |
|--------|--------|
| 1) | 680.00 yd³ |
| 2) | 709.33 ft³ |
| 3) | 275.00 in³ |
| 4) | 16.00 m³ |
| 5) | 163.33 yd³ |
| 6) | 346.67 ft³ |
| 7) | 298.67 ft³ |
| 8) | 726.00 in³ |
| 9) | 680.00 yd³ |

> Note: Always make sure units are consistent and that you're using the correct base area (whether it's a rectangle, triangle, etc.) and the perpendicular height from the apex to the base.

Let me know if you'd like this as a printable answer sheet!