Grade 5 Geometry worksheet on calculating the volume of rectangular prisms.

Let's solve each problem step by step using the formula for the volume of a rectangular prism:

$$
\text{Volume} = \text{length} \times \text{width} \times \text{height}
$$

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Problem 1:

- Dimensions: 4 in (length), 6 in (height), and 4 in (width)
- Volume = $ 4 \times 6 \times 4 $
- $ = 24 \times 4 = 96 $ in³

✔ Answer: Volume = 96 in³

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Problem 2:

- Given: Volume = 90 in³, height = 6 in, width = 3 in, length = x in
- Use formula: $ V = l \times w \times h $
- $ 90 = x \times 3 \times 6 $
- $ 90 = 18x $
- $ x = \frac{90}{18} = 5 $

✔ Answer: $ x = 5 $ in

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Problem 3:

- Dimensions: 7 m (height), 8 m (length), 3 m (width)
- Volume = $ 7 \times 8 \times 3 $
- $ = 56 \times 3 = 168 $ m³

✔ Answer: Volume = 168 m³

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Problem 4:

- Given: Volume = 98 cm³, height = 7 cm, width = y cm, length = 7 cm
- $ V = l \times w \times h $
- $ 98 = 7 \times y \times 7 $
- $ 98 = 49y $
- $ y = \frac{98}{49} = 2 $

✔ Answer: $ y = 2 $ cm

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Problem 5:

- Given: Volume = 60 ft³, height = 4 ft, width = 7.5 ft, length = z ft
- $ 60 = z \times 7.5 \times 4 $
- $ 60 = z \times 30 $
- $ z = \frac{60}{30} = 2 $

✔ Answer: $ z = 2 $ ft

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Problem 6:

- Dimensions: 9 in (length), 9 in (width), 9 in (height)
- This is a cube!
- Volume = $ 9 \times 9 \times 9 = 729 $ in³

✔ Answer: Volume = 729 in³

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✔ Final Answers:

1. 96 in³
2. x = 5 in
3. 168 m³
4. y = 2 cm
5. z = 2 ft
6. 729 in³

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