Volume of Rectangular Pyramids | Printable Worksheets - Free Printable

Sure! Let’s solve each problem step by step. The formula for the volume of a rectangular pyramid is:

> V = (1/3) × Length × Width × Height

We’ll apply this formula to each problem, making sure units are consistent and rounding to two decimal places as instructed.

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## Part A: Find volume from diagrams

Problem 1

- Diagram shows:
- Base: 2 in × 4 in → so Length = 4 in, Width = 2 in
- Height = 5 in

Volume = (1/3) × 4 × 2 × 5 = (1/3) × 40 = 13.33 in³

✔ Answer: 13.33 in³

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Problem 2

- Diagram shows:
- Base: 6 ft × 20 ft → Length = 20 ft, Width = 6 ft
- Height = 8 ft

Volume = (1/3) × 20 × 6 × 8 = (1/3) × 960 = 320.00 ft³

✔ Answer: 320.00 ft³

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Problem 3

- Diagram shows:
- Base: 10 yd × 7 yd → Length = 10 yd, Width = 7 yd
- Height = 22 yd

Volume = (1/3) × 10 × 7 × 22 = (1/3) × 1540 ≈ 513.33 yd³

✔ Answer: 513.33 yd³

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## Part B: Find volume from given parameters

Problem 4

- Width = 25 in
- Height = 21 in
- Length = 1 yd → Convert to inches: 1 yd = 36 in

Volume = (1/3) × 36 × 25 × 21 = (1/3) × 18900 = 6300.00 in³

✔ Answer: 6300.00 in³

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Problem 5

- Length = 30 ft
- Width = 9 ft
- Height = 13 yd → Convert to feet: 13 yd = 13 × 3 = 39 ft

Volume = (1/3) × 30 × 9 × 39 = (1/3) × 10530 = 3510.00 ft³

✔ Answer: 3510.00 ft³

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Problem 6

- Height = 18 in
- Length = 5 yd → 5 × 36 = 180 in
- Width = 3 yd → 3 × 36 = 108 in

Volume = (1/3) × 180 × 108 × 18

First: 180 × 108 = 19440
Then: 19440 × 18 = 349920
Then: ÷ 3 = 116640.00 in³

✔ Answer: 116640.00 in³

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Problem 7

- Width = 30 ft
- Length = 11 yd → 11 × 3 = 33 ft
- Height = 26 yd → 26 × 3 = 78 ft

Volume = (1/3) × 33 × 30 × 78

First: 33 × 30 = 990
Then: 990 × 78 = 77220
Then: ÷ 3 = 25740.00 ft³

✔ Answer: 25740.00 ft³

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## Problem 8: Word Problem

> The length, width and height of a rectangular pyramid are 27 inches, 1 foot and 29 inches respectively. What is the volume in cubic inches?

- First, convert all to inches:
- Length = 27 in
- Width = 1 ft = 12 in
- Height = 29 in

Volume = (1/3) × 27 × 12 × 29

Step-by-step:
- 27 × 12 = 324
- 324 × 29 = let’s compute:
300 × 29 = 8700
24 × 29 = 696
Total = 8700 + 696 = 9396
- Divide by 3: 9396 ÷ 3 = 3132.00 in³

✔ Answer: 3132.00 in³

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## ✔ Final Answers Summary:

Part A:

1) 13.33 in³
2) 320.00 ft³
3) 513.33 yd³

Part B:

4) 6300.00 in³
5) 3510.00 ft³
6) 116640.00 in³
7) 25740.00 ft³
8) 3132.00 in³

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Let me know if you’d like to see the calculations written out differently or need help with unit conversions!