Worksheet on Volume of a Cube and Cuboid |The Volume of a RectangleBox - Free Printable
Educational worksheet: Worksheet on Volume of a Cube and Cuboid |The Volume of a RectangleBox. Download and print for classroom or home learning activities.
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Step-by-step solution for: Worksheet on Volume of a Cube and Cuboid |The Volume of a RectangleBox
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Show Answer Key & Explanations
Step-by-step solution for: Worksheet on Volume of a Cube and Cuboid |The Volume of a RectangleBox
It looks like you've uploaded an image showing six rectangular prisms (also known as cuboids), each labeled with dimensions. The task likely involves calculating surface area or volume of each cuboid, though the exact instruction isn't specified in your message.
Since no specific question was asked, I’ll assume the goal is to calculate the surface area and volume for each of the six cuboids shown.
---
For a rectangular prism with length $ l $, width $ w $, and height $ h $:
- Volume = $ V = l \times w \times h $
- Surface Area = $ SA = 2(lw + lh + wh) $
Let’s go through each one.
---
- $ l = 7 $, $ w = 6 $, $ h = 2 $
Volume:
$$
V = 7 \times 6 \times 2 = 84 \text{ cm}^3
$$
Surface Area:
$$
SA = 2(7×6 + 7×2 + 6×2) = 2(42 + 14 + 12) = 2(68) = 136 \text{ cm}^2
$$
---
- $ l = 4 $, $ w = 3 $, $ h = 2 $
Volume:
$$
V = 4 \times 3 \times 2 = 24 \text{ cm}^3
$$
Surface Area:
$$
SA = 2(4×3 + 4×2 + 3×2) = 2(12 + 8 + 6) = 2(26) = 52 \text{ cm}^2
$$
---
- $ l = 10 $, $ w = 6 $, $ h = 4 $
Volume:
$$
V = 10 \times 6 \times 4 = 240 \text{ cm}^3
$$
Surface Area:
$$
SA = 2(10×6 + 10×4 + 6×4) = 2(60 + 40 + 24) = 2(124) = 248 \text{ cm}^2
$$
---
- $ l = 12 $, $ w = 5 $, $ h = 2 $
Volume:
$$
V = 12 \times 5 \times 2 = 120 \text{ cm}^3
$$
Surface Area:
$$
SA = 2(12×5 + 12×2 + 5×2) = 2(60 + 24 + 10) = 2(94) = 188 \text{ cm}^2
$$
---
- $ l = 15 $, $ w = 6 $, $ h = 8.5 $
Volume:
$$
V = 15 \times 6 \times 8.5 = 90 \times 8.5 = 765 \text{ cm}^3
$$
Surface Area:
$$
SA = 2(15×6 + 15×8.5 + 6×8.5) = 2(90 + 127.5 + 51) = 2(268.5) = 537 \text{ cm}^2
$$
---
- $ l = 7.5 $, $ w = 4.5 $, $ h = 7.5 $
Volume:
$$
V = 7.5 \times 4.5 \times 7.5
$$
First compute $ 7.5 \times 7.5 = 56.25 $, then:
$$
56.25 \times 4.5 = 253.125 \text{ cm}^3
$$
Surface Area:
$$
SA = 2(7.5×4.5 + 7.5×7.5 + 4.5×7.5)
= 2(33.75 + 56.25 + 33.75)
= 2(123.75) = 247.5 \text{ cm}^2
$$
---
| Cuboid | Dimensions (cm) | Volume (cm³) | Surface Area (cm²) |
|--------|-------------------------|--------------|----------------------|
| (i) | 7 × 6 × 2 | 84 | 136 |
| (ii) | 4 × 3 × 2 | 24 | 52 |
| (iii) | 10 × 6 × 4 | 240 | 248 |
| (iv) | 12 × 5 × 2 | 120 | 188 |
| (v) | 15 × 6 × 8.5 | 765 | 537 |
| (vi) | 7.5 × 4.5 × 7.5 | 253.125 | 247.5 |
---
- If your original problem asked only for volume, then just use the volume column.
- If it asked for surface area, use the SA column.
- If it asked for both, this table gives all values.
- If the task was something else (like comparing volumes, finding total surface area of all, etc.), let me know and I can adjust accordingly!
Let me know if you want this formatted differently or need help visualizing any part!
Since no specific question was asked, I’ll assume the goal is to calculate the surface area and volume for each of the six cuboids shown.
---
🔷 General Formulas:
For a rectangular prism with length $ l $, width $ w $, and height $ h $:
- Volume = $ V = l \times w \times h $
- Surface Area = $ SA = 2(lw + lh + wh) $
Let’s go through each one.
---
✔ (i) Dimensions: 7 cm × 6 cm × 2 cm
- $ l = 7 $, $ w = 6 $, $ h = 2 $
Volume:
$$
V = 7 \times 6 \times 2 = 84 \text{ cm}^3
$$
Surface Area:
$$
SA = 2(7×6 + 7×2 + 6×2) = 2(42 + 14 + 12) = 2(68) = 136 \text{ cm}^2
$$
---
✔ (ii) Dimensions: 4 cm × 3 cm × 2 cm
- $ l = 4 $, $ w = 3 $, $ h = 2 $
Volume:
$$
V = 4 \times 3 \times 2 = 24 \text{ cm}^3
$$
Surface Area:
$$
SA = 2(4×3 + 4×2 + 3×2) = 2(12 + 8 + 6) = 2(26) = 52 \text{ cm}^2
$$
---
✔ (iii) Dimensions: 10 cm × 6 cm × 4 cm
- $ l = 10 $, $ w = 6 $, $ h = 4 $
Volume:
$$
V = 10 \times 6 \times 4 = 240 \text{ cm}^3
$$
Surface Area:
$$
SA = 2(10×6 + 10×4 + 6×4) = 2(60 + 40 + 24) = 2(124) = 248 \text{ cm}^2
$$
---
✔ (iv) Dimensions: 12 cm × 5 cm × 2 cm
- $ l = 12 $, $ w = 5 $, $ h = 2 $
Volume:
$$
V = 12 \times 5 \times 2 = 120 \text{ cm}^3
$$
Surface Area:
$$
SA = 2(12×5 + 12×2 + 5×2) = 2(60 + 24 + 10) = 2(94) = 188 \text{ cm}^2
$$
---
✔ (v) Dimensions: 15 cm × 6 cm × 8.5 cm
- $ l = 15 $, $ w = 6 $, $ h = 8.5 $
Volume:
$$
V = 15 \times 6 \times 8.5 = 90 \times 8.5 = 765 \text{ cm}^3
$$
Surface Area:
$$
SA = 2(15×6 + 15×8.5 + 6×8.5) = 2(90 + 127.5 + 51) = 2(268.5) = 537 \text{ cm}^2
$$
---
✔ (vi) Dimensions: 7.5 cm × 4.5 cm × 7.5 cm
- $ l = 7.5 $, $ w = 4.5 $, $ h = 7.5 $
Volume:
$$
V = 7.5 \times 4.5 \times 7.5
$$
First compute $ 7.5 \times 7.5 = 56.25 $, then:
$$
56.25 \times 4.5 = 253.125 \text{ cm}^3
$$
Surface Area:
$$
SA = 2(7.5×4.5 + 7.5×7.5 + 4.5×7.5)
= 2(33.75 + 56.25 + 33.75)
= 2(123.75) = 247.5 \text{ cm}^2
$$
---
📊 Summary Table:
| Cuboid | Dimensions (cm) | Volume (cm³) | Surface Area (cm²) |
|--------|-------------------------|--------------|----------------------|
| (i) | 7 × 6 × 2 | 84 | 136 |
| (ii) | 4 × 3 × 2 | 24 | 52 |
| (iii) | 10 × 6 × 4 | 240 | 248 |
| (iv) | 12 × 5 × 2 | 120 | 188 |
| (v) | 15 × 6 × 8.5 | 765 | 537 |
| (vi) | 7.5 × 4.5 × 7.5 | 253.125 | 247.5 |
---
💡 Final Notes:
- If your original problem asked only for volume, then just use the volume column.
- If it asked for surface area, use the SA column.
- If it asked for both, this table gives all values.
- If the task was something else (like comparing volumes, finding total surface area of all, etc.), let me know and I can adjust accordingly!
Let me know if you want this formatted differently or need help visualizing any part!
Parent Tip: Review the logic above to help your child master the concept of surface area of a cube worksheet.
