Grade 6 Worksheets: Volume & surface area of rectangular prisms ... - Free Printable

Let's solve the Rectangular Prism - Volume & Surface Area worksheet step by step. The goal is to find both the volume and surface area for each of the four rectangular prisms shown.

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🔷 Formulas Used:

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) $

We'll use these formulas for each problem.

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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

This is a square prism (since two dimensions 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 = 5 in
- Width = 3 in
- Height = 4 in

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

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

✔ 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 (\text{side})^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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📝 Explanation:

- Volume measures how much space the prism occupies (cubic units).
- Surface Area measures the total area of all six faces (square units).
- Always label your answers with correct units: in³ for volume, in² for surface area.
- Double-check multiplication and addition steps to avoid errors.

Let me know if you'd like this as a printable answer key or need help visualizing any of the prisms!