Grade 6 Geometry Worksheet: Find the volume and surface area of rectangular prisms.

Let's solve the Rectangular Prism - Volume & Surface Area worksheet step by step.

We are given four rectangular prisms (also called cuboids), and for each, we need to calculate:

1. Volume
2. Surface Area

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🔷 Formulas:

For a rectangular prism with length $ l $, width $ w $, and height $ h $:

- Volume = $ V = l \times w \times h $
- Surface Area = $ SA = 2(lw + lh + wh) $

All dimensions are in inches (in).

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✔ Problem 1:

Dimensions:
- Length = 7 in
- Width = 3 in
- Height = 6 in

#### Volume:
$$
V = 7 \times 3 \times 6 = 126 \text{ in}^3
$$

#### Surface Area:
$$
SA = 2(7 \times 3 + 7 \times 6 + 3 \times 6) = 2(21 + 42 + 18) = 2(81) = 162 \text{ in}^2
$$

✔ Answer:
- Volume = 126 in³
- Surface Area = 162 in²

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✔ Problem 2:

Dimensions:
- Length = 8 in
- Width = 8 in
- Height = 4 in

Note: This is a rectangular prism (not a cube), since not all sides are equal.

#### Volume:
$$
V = 8 \times 8 \times 4 = 256 \text{ in}^3
$$

#### Surface Area:
$$
SA = 2(8 \times 8 + 8 \times 4 + 8 \times 4) = 2(64 + 32 + 32) = 2(128) = 256 \text{ in}^2
$$

✔ Answer:
- Volume = 256 in³
- Surface Area = 256 in²

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✔ Problem 3:

Dimensions:
- Length = 3 in
- Width = 4 in
- Height = 5 in

#### Volume:
$$
V = 3 \times 4 \times 5 = 60 \text{ in}^3
$$

#### Surface Area:
$$
SA = 2(3 \times 4 + 3 \times 5 + 4 \times 5) = 2(12 + 15 + 20) = 2(47) = 94 \text{ in}^2
$$

✔ Answer:
- Volume = 60 in³
- Surface Area = 94 in²

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✔ Problem 4:

Dimensions:
- Length = 6 in
- Width = 6 in
- Height = 6 in

This is a cube (all sides equal).

#### Volume:
$$
V = 6 \times 6 \times 6 = 216 \text{ in}^3
$$

#### Surface Area:
$$
SA = 2(6 \times 6 + 6 \times 6 + 6 \times 6) = 2(36 + 36 + 36) = 2(108) = 216 \text{ in}^2
$$

Alternatively, for a cube: $ SA = 6 \times s^2 = 6 \times 36 = 216 $

✔ Answer:
- Volume = 216 in³
- Surface Area = 216 in²

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📝 Final Answers Summary:

| Problem | Volume (in³) | Surface Area (in²) |
|--------|--------------|---------------------|
| 1 | 126 | 162 |
| 2 | 256 | 256 |
| 3 | 60 | 94 |
| 4 | 216 | 216 |

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