Let’s solve each part step by step.
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Part 1: Rectangular prisms built from centimeter cubes
We count the number of cubes along each dimension to find length, width, and height. Then multiply them to get volume (since each cube is 1 cm³).
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a. First prism (top left)
Looking at the figure:
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Length: Count cubes along the longest side on top → 6 cubes →
6 cm
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Width: Count cubes going into the page (side view) → 2 cubes →
2 cm
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Height: Count layers vertically → 2 layers →
2 cm
Volume = Length × Width × Height
= 6 × 2 × 2 =
24 cm³
✔ Check: 6×2=12, 12×2=24 → correct.
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b. Second prism (top right)
This one looks like a cube but let’s check:
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Length: Front face horizontal → 3 cubes →
3 cm
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Width: Side going back → 3 cubes →
3 cm
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Height: Vertical layers → 4 cubes →
4 cm
Wait — actually, looking again: it has 3 columns front-to-back? Let me recount carefully.
Actually, in the drawing:
Front face: 3 across (length), 4 up (height).
Depth (width): you can see 3 cubes deep on the side.
So:
- Length = 3 cm
- Width = 3 cm
- Height = 4 cm
Volume = 3 × 3 × 4 = 9 × 4 =
36 cm³
✔ Check: 3×3=9, 9×4=36 → correct.
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Part 2: Calculate volume with given dimensions
Formula: Volume = length × width × height
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a. Prism with inches
Dimensions: 4 in (length), 3 in (width), 4 in (height)
V = 4 × 3 × 4
First: 4 × 3 = 12
Then: 12 × 4 =
48 in³
✔ Correct.
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b. Prism with meters
Dimensions: 3 m (length), 2 m (width), 6 m (height)
V = 3 × 2 × 6
First: 3 × 2 = 6
Then: 6 × 6 =
36 m³
✔ Correct.
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Final Answer:
Top Section:
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:
a. V = 48 in³
b. V = 36 m³
Parent Tip: Review the logic above to help your child master the concept of volume worksheet 6th grade.
