Let's solve the problem step by step.
We are asked to find the
Volume and
Surface Area for several
rectangular prisms and
cubes.
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🔷 Formulas:
#### For a
Rectangular Prism (length × width × height):
-
Volume = $ V = l \times w \times h $
-
Surface Area = $ SA = 2(lw + lh + wh) $
#### For a
Cube (all sides equal, side = s):
-
Volume = $ V = s^3 $
-
Surface Area = $ SA = 6s^2 $
---
##
✔ Section A: Rectangular Prisms
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1. Dimensions: 2 cm × 3 cm × 5 cm
-
Volume = $ 2 \times 3 \times 5 = 30 \text{ cm}^3 $
-
Surface Area = $ 2(2×3 + 2×5 + 3×5) = 2(6 + 10 + 15) = 2(31) = 62 \text{ cm}^2 $
✔ Volume:
30 cm³, Surface Area:
62 cm²
---
2. Dimensions: 2 cm × 9 cm × 3 cm
-
Volume = $ 2 \times 9 \times 3 = 54 \text{ cm}^3 $
-
Surface Area = $ 2(2×9 + 2×3 + 9×3) = 2(18 + 6 + 27) = 2(51) = 102 \text{ cm}^2 $
✔ Volume:
54 cm³, Surface Area:
102 cm²
---
3. Dimensions: 4 m × 4 m × 12 m
-
Volume = $ 4 \times 4 \times 12 = 192 \text{ m}^3 $
-
Surface Area = $ 2(4×4 + 4×12 + 4×12) = 2(16 + 48 + 48) = 2(112) = 224 \text{ m}^2 $
✔ Volume:
192 m³, Surface Area:
224 m²
---
4. Dimensions: 70 mm × 110 mm × 20 mm
-
Volume = $ 70 \times 110 \times 20 = 154,000 \text{ mm}^3 $
-
Surface Area = $ 2(70×110 + 70×20 + 110×20) = 2(7700 + 1400 + 2200) = 2(11300) = 22,600 \text{ mm}^2 $
✔ Volume:
154,000 mm³, Surface Area:
22,600 mm²
---
##
✔ Cube Section
---
1. Side = 6 cm
-
Volume = $ 6^3 = 216 \text{ cm}^3 $
-
Surface Area = $ 6 \times 6^2 = 6 \times 36 = 216 \text{ cm}^2 $
✔ Volume:
216 cm³, Surface Area:
216 cm²
---
2. Side = 30 mm
-
Volume = $ 30^3 = 27,000 \text{ mm}^3 $
-
Surface Area = $ 6 \times 30^2 = 6 \times 900 = 5,400 \text{ mm}^2 $
✔ Volume:
27,000 mm³, Surface Area:
5,400 mm²
---
3. Side = 8 m
-
Volume = $ 8^3 = 512 \text{ m}^3 $
-
Surface Area = $ 6 \times 8^2 = 6 \times 64 = 384 \text{ m}^2 $
✔ Volume:
512 m³, Surface Area:
384 m²
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4. Side = 5 cm
-
Volume = $ 5^3 = 125 \text{ cm}^3 $
-
Surface Area = $ 6 \times 5^2 = 6 \times 25 = 150 \text{ cm}^2 $
✔ Volume:
125 cm³, Surface Area:
150 cm²
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## 📊 Final Table (Completed)
| Rectangular Prism | Volume | Surface Area |
|-------------------|--------|--------------|
| 2×3×5 cm | 30 cm³ | 62 cm² |
| 2×9×3 cm | 54 cm³ | 102 cm² |
| 4×4×12 m | 192 m³ | 224 m² |
| 70×110×20 mm | 154,000 mm³ | 22,600 mm² |
| Cube | Volume | Surface Area |
|------|--------|--------------|
| 6 cm | 216 cm³ | 216 cm² |
| 30 mm | 27,000 mm³ | 5,400 mm² |
| 8 m | 512 m³ | 384 m² |
| 5 cm | 125 cm³ | 150 cm² |
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✔ All calculations are correct and consistent with geometry formulas.
Let me know if you'd like this formatted as a printable table or need help with units conversion!
Parent Tip: Review the logic above to help your child master the concept of surface area and volume of a rectangular prism worksheet.
