Let’s solve each part step by step.
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Part 1: Counting cubes to find dimensions and volume
Each small cube is 1 cm on each side, so we can count how many cubes are along the length, width, and height.
a. First prism (top left)
- Look at the front face: there are
6 cubes across → that’s the
length = 6 cm
- The depth (going back) has
2 cubes → that’s the
width = 2 cm
- There are
2 layers high → that’s the
height = 2 cm
Volume = Length × Width × Height
= 6 × 2 × 2
= 12 × 2
=
24 cm³
✔ Double-check: You could also count all the little cubes — 6 in a row, 2 rows deep, 2 layers high → 6×2×2 = 24 cubes → 24 cm³. Correct!
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b. Second prism (top right)
- Front face:
3 cubes across →
length = 3 cm
- Depth:
3 cubes going back →
width = 3 cm
- Height:
4 layers up →
height = 4 cm
Volume = 3 × 3 × 4
= 9 × 4
=
36 cm³
✔ Double-check: 3×3=9 per layer, 4 layers → 9×4=36. Correct!
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Part 2: Using given measurements to calculate volume
Formula still applies: Volume = Length × Width × Height
Just multiply the numbers given — don’t forget units!
a. Cube-like shape with inches
Given:
- Length = 4 in
- Width = 3 in
- Height = 4 in
Volume = 4 × 3 × 4
= 12 × 4
=
48 in³
✔ Check: 4×3=12, times 4 again = 48. Units are cubic inches → in³. Good.
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b. Tall rectangular prism with meters
Given:
- Length = 3 m
- Width = 2 m
- Height = 6 m
Volume = 3 × 2 × 6
= 6 × 6
=
36 m³
✔ Check: 3×2=6, times 6 = 36. Units are cubic meters → m³. Perfect.
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Final Answer:
Top Section (counting cubes):
a.
Length: 6 cm
Width: 2 cm
Height: 2 cm
Volume: 24 cm³
b.
Length: 3 cm
Width: 3 cm
Height: 4 cm
Volume: 36 cm³
Bottom Section (given measurements):
a. V = 48 in³
b. V = 36 m³
Parent Tip: Review the logic above to help your child master the concept of volume of rectangular prism worksheet.
