Let's solve each problem on the
Rectangular Prism - Volume & Surface Area worksheet step by step.
We are given four rectangular prisms (also known as boxes), and for each, we need to calculate:
1.
Volume = length × width × height
2.
Surface Area = 2(lw + lh + wh)
---
🔷 Problem 1:
Dimensions:
- Length = 3 in
- Width = 3 in
- Height = 2 in
####
✔ Volume:
$$
V = l \times w \times h = 3 \times 3 \times 2 = 18 \text{ in}^3
$$
####
✔ Surface Area:
$$
SA = 2(lw + lh + wh) = 2(3×3 + 3×2 + 3×2) = 2(9 + 6 + 6) = 2(21) = 42 \text{ in}^2
$$
✔ Answer:
- Volume:
18 in³
- Surface Area:
42 in²
---
🔷 Problem 2:
Dimensions:
- Length = 4 in
- Width = 2 in
- Height = 2 in
####
✔ Volume:
$$
V = 4 × 2 × 2 = 16 \text{ in}^3
$$
####
✔ Surface Area:
$$
SA = 2(4×2 + 4×2 + 2×2) = 2(8 + 8 + 4) = 2(20) = 40 \text{ in}^2
$$
✔ Answer:
- Volume:
16 in³
- Surface Area:
40 in²
---
🔷 Problem 3:
Dimensions:
- Length = 5 in
- Width = 5 in
- Height = 5 in
This is a
cube!
####
✔ Volume:
$$
V = 5 × 5 × 5 = 125 \text{ in}^3
$$
####
✔ Surface Area:
Since all sides are equal:
$$
SA = 6 × (side)^2 = 6 × 25 = 150 \text{ in}^2
$$
Or using formula:
$$
SA = 2(5×5 + 5×5 + 5×5) = 2(25 + 25 + 25) = 2(75) = 150 \text{ in}^2
$$
✔ Answer:
- Volume:
125 in³
- Surface Area:
150 in²
---
🔷 Problem 4:
Dimensions:
- Length = 5 in
- Width = 2 in
- Height = 6 in
####
✔ Volume:
$$
V = 5 × 2 × 6 = 60 \text{ in}^3
$$
####
✔ Surface Area:
$$
SA = 2(5×2 + 5×6 + 2×6) = 2(10 + 30 + 12) = 2(52) = 104 \text{ in}^2
$$
✔ Answer:
- Volume:
60 in³
- Surface Area:
104 in²
---
✔ Final Answers Summary:
| Problem | Volume | Surface Area |
|--------|--------------|--------------|
| 1 | 18 in³ | 42 in² |
| 2 | 16 in³ | 40 in² |
| 3 | 125 in³ | 150 in² |
| 4 | 60 in³ | 104 in² |
---
📝 Explanation of Concepts:
-
Volume tells us how much space the prism occupies (in cubic units).
-
Surface Area is the total area of all six faces (in square units).
- For a rectangular prism:
- Volume = $ l \times w \times h $
- Surface Area = $ 2(lw + lh + wh) $
These formulas work for all rectangular prisms, including cubes (which are special cases where all sides are equal).
Let me know if you'd like this formatted into a printable answer sheet!
Parent Tip: Review the logic above to help your child master the concept of finding area and volume worksheet.
