Let's solve each problem step by step using the formula for the
volume of a rectangular prism:
>
Volume = length × width × height
> or
>
V = l × w × h
Each small cube represents
1 cm³, so we can count the cubes or use the dimensions given.
---
Problem 1
Given:
- Length = 4 cm
- Width = 1 cm
- Height = 3 cm
We are told:
- The base is 4 cm long (along the bottom)
- The depth (width) is 1 cm
- The height is 3 cm (stacked up)
Now calculate the volume:
> Volume = 4 × 1 × 3 =
12 cm³
✔ Answer:
- Length:
4 cm
- Width:
1 cm
- Height:
3 cm
- Volume:
4 × 1 × 3 = 12 cm³
---
Problem 2
This is a cube-like structure. Let’s count the cubes:
- It has
3 layers (height = 3 cm)
- Each layer is
2 × 2 cubes (so length = 2 cm, width = 2 cm)
So:
- Length = 2 cm
- Width = 2 cm
- Height = 3 cm
Volume = 2 × 2 × 3 =
12 cm³
✔ Answer:
- Length:
2 cm
- Width:
2 cm
- Height:
3 cm
- Volume:
2 × 2 × 3 = 12 cm³
---
Problem 3
Looking at the shape:
- It has
3 columns along the length → length = 3 cm
-
2 rows in width → width = 2 cm
-
2 layers high → height = 2 cm
So:
- Length = 3 cm
- Width = 2 cm
- Height = 2 cm
Volume = 3 × 2 × 2 =
12 cm³
✔ Answer:
- Length:
3 cm
- Width:
2 cm
- Height:
2 cm
- Volume:
3 × 2 × 2 = 12 cm³
---
✔ Final Answers:
####
1)
- Length:
4 cm
- Width:
1 cm
- Height:
3 cm
- Volume:
4 × 1 × 3 = 12 cm³
####
2)
- Length:
2 cm
- Width:
2 cm
- Height:
3 cm
- Volume:
2 × 2 × 3 = 12 cm³
####
3)
- Length:
3 cm
- Width:
2 cm
- Height:
2 cm
- Volume:
3 × 2 × 2 = 12 cm³
---
🔍 Summary:
All three prisms have the same volume (
12 cm³) but different dimensions — this shows that different shapes can have the same volume.
Let me know if you'd like a visual explanation or help printing this!
Parent Tip: Review the logic above to help your child master the concept of volume math worksheet.
