Let's solve the
Rectangular Prism - Volume & Surface Area worksheet step by step. We’ll calculate both the
volume and
surface area for each of the four rectangular prisms shown.
---
🔷 Formulas:
-
Volume (V) of a rectangular prism:
$$
V = \text{length} \times \text{width} \times \text{height}
$$
-
Surface Area (SA) of a rectangular prism:
$$
SA = 2(lw + lh + wh)
$$
Where:
- $ l $ = length
- $ w $ = width
- $ h $ = height
---
##
✔ Problem 1:
Dimensions:
- Length = 3 in
- Width = 3 in
- Height = 2 in
Volume:
$$
V = 3 \times 3 \times 2 = 18 \text{ in}^3
$$
Surface Area:
$$
SA = 2(3 \cdot 3 + 3 \cdot 2 + 3 \cdot 2) = 2(9 + 6 + 6) = 2(21) = 42 \text{ in}^2
$$
✔ Answer:
- Volume =
18 in³
- Surface Area =
42 in²
---
##
✔ Problem 2:
Dimensions:
- Length = 4 in
- Width = 2 in
- Height = 2 in
Volume:
$$
V = 4 \times 2 \times 2 = 16 \text{ in}^3
$$
Surface Area:
$$
SA = 2(4 \cdot 2 + 4 \cdot 2 + 2 \cdot 2) = 2(8 + 8 + 4) = 2(20) = 40 \text{ in}^2
$$
✔ Answer:
- Volume =
16 in³
- Surface Area =
40 in²
---
##
✔ Problem 3:
Dimensions:
- Length = 5 in
- Width = 5 in
- Height = 5 in
This is a
cube (all sides equal).
Volume:
$$
V = 5 \times 5 \times 5 = 125 \text{ in}^3
$$
Surface Area:
$$
SA = 2(5 \cdot 5 + 5 \cdot 5 + 5 \cdot 5) = 2(25 + 25 + 25) = 2(75) = 150 \text{ in}^2
$$
✔ Answer:
- Volume =
125 in³
- Surface Area =
150 in²
---
##
✔ Problem 4:
Dimensions:
- Length = 5 in
- Width = 2 in
- Height = 5 in
Volume:
$$
V = 5 \times 2 \times 5 = 50 \text{ in}^3
$$
Surface Area:
$$
SA = 2(5 \cdot 2 + 5 \cdot 5 + 2 \cdot 5) = 2(10 + 25 + 10) = 2(45) = 90 \text{ in}^2
$$
✔ Answer:
- Volume =
50 in³
- Surface Area =
90 in²
---
📝 Final Answers Summary:
| Problem | Volume (in³) | Surface Area (in²) |
|--------|--------------|---------------------|
| 1 | 18 | 42 |
| 2 | 16 | 40 |
| 3 | 125 | 150 |
| 4 | 50 | 90 |
---
💡 Tips for Students:
- Always label the dimensions clearly.
- Double-check multiplication.
- Remember: surface area adds up all six faces (top/bottom, front/back, left/right).
- For cubes, you can use $ V = s^3 $ and $ SA = 6s^2 $ as shortcuts.
Let me know if you'd like this as a printable answer sheet! 😊
Parent Tip: Review the logic above to help your child master the concept of volume of cube and rectangular prism worksheet.
