Volume and Surface Area of Rectangular Prisms Worksheet | 7th ... - Free Printable

To solve this problem, we need to calculate the Volume and Surface Area for each shape listed in the worksheet.

Here are the formulas we will use:
* Volume of a Rectangular Prism: $V = \text{length} \times \text{width} \times \text{height}$
* Surface Area of a Rectangular Prism: $SA = 2(\text{length} \times \text{width} + \text{length} \times \text{height} + \text{width} \times \text{height})$
* Volume of a Cube: $V = \text{side} \times \text{side} \times \text{side}$ (or $s^3$)
* Surface Area of a Cube: $SA = 6 \times (\text{side} \times \text{side})$ (or $6s^2$)

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Section A: Rectangular Prisms

1. First Prism
* Dimensions: Length = 5cm, Width = 3cm, Height = 2cm
* Volume: $5 \times 3 \times 2 = 30$
* Answer: $30\text{ cm}^3$
* Surface Area:
* $2 \times (5 \times 3 + 5 \times 2 + 3 \times 2)$
* $2 \times (15 + 10 + 6)$
* $2 \times 31 = 62$
* Answer: $62\text{ cm}^2$

2. Second Prism
* Dimensions: Length = 9cm, Width = 3cm, Height = 2cm
* Volume: $9 \times 3 \times 2 = 54$
* Answer: $54\text{ cm}^3$
* Surface Area:
* $2 \times (9 \times 3 + 9 \times 2 + 3 \times 2)$
* $2 \times (27 + 18 + 6)$
* $2 \times 51 = 102$
* Answer: $102\text{ cm}^2$

3. Third Prism
* Dimensions: Length = 12m, Width = 4m, Height = 4m
* Volume: $12 \times 4 \times 4 = 192$
* Answer: $192\text{ m}^3$
* Surface Area:
* $2 \times (12 \times 4 + 12 \times 4 + 4 \times 4)$
* $2 \times (48 + 48 + 16)$
* $2 \times 112 = 224$
* Answer: $224\text{ m}^2$

4. Fourth Prism
* Dimensions: Length = 110mm, Width = 20mm, Height = 70mm
* Volume: $110 \times 20 \times 70$
* $2200 \times 70 = 154,000$
* Answer: $154,000\text{ mm}^3$
* Surface Area:
* $2 \times (110 \times 20 + 110 \times 70 + 20 \times 70)$
* $2 \times (2,200 + 7,700 + 1,400)$
* $2 \times 11,300 = 22,600$
* Answer: $22,600\text{ mm}^2$

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Section B: Cubes

1. First Cube
* Dimensions: Side = 6cm
* Volume: $6 \times 6 \times 6 = 216$
* Answer: $216\text{ cm}^3$
* Surface Area: $6 \times (6 \times 6) = 6 \times 36 = 216$
* Answer: $216\text{ cm}^2$

2. Second Cube
* Dimensions: Side = 30mm
* Volume: $30 \times 30 \times 30 = 27,000$
* Answer: $27,000\text{ mm}^3$
* Surface Area: $6 \times (30 \times 30) = 6 \times 900 = 5,400$
* Answer: $5,400\text{ mm}^2$

3. Third Cube
* Dimensions: Side = 8m
* Volume: $8 \times 8 \times 8 = 512$
* Answer: $512\text{ m}^3$
* Surface Area: $6 \times (8 \times 8) = 6 \times 64 = 384$
* Answer: $384\text{ m}^2$

4. Fourth Cube
* Dimensions: Side = 5cm
* Volume: $5 \times 5 \times 5 = 125$
* Answer: $125\text{ cm}^3$
* Surface Area: $6 \times (5 \times 5) = 6 \times 25 = 150$
* Answer: $150\text{ cm}^2$

Final Answer:
Rectangular Prisms:
1. Volume: $30\text{ cm}^3$, Surface Area: $62\text{ cm}^2$
2. Volume: $54\text{ cm}^3$, Surface Area: $102\text{ cm}^2$
3. Volume: $192\text{ m}^3$, Surface Area: $224\text{ m}^2$
4. Volume: $154,000\text{ mm}^3$, Surface Area: $22,600\text{ mm}^2$

Cubes:
1. Volume: $216\text{ cm}^3$, Surface Area: $216\text{ cm}^2$
2. Volume: $27,000\text{ mm}^3$, Surface Area: $5,400\text{ mm}^2$
3. Volume: $512\text{ m}^3$, Surface Area: $384\text{ m}^2$
4. Volume: $125\text{ cm}^3$, Surface Area: $150\text{ cm}^2$