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

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

Formulas:
* Rectangular Prism:
* Volume = Length × Width × Height ($V = l \times w \times h$)
* Surface Area = $2(lw + lh + wh)$
* Cube (Special prism where all sides are equal):
* Volume = Side × Side × Side ($V = s^3$)
* Surface Area = $6 \times (\text{Side} \times \text{Side})$ ($SA = 6s^2$)

Let's go through each row step-by-step.

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Section A: Rectangular Prisms

1. First Shape
* Dimensions: $2\text{ cm}$, $3\text{ cm}$, $5\text{ cm}$
* Volume: $2 \times 3 \times 5 = 30$. So, $30\text{ cm}^3$.
* Surface Area:
* Faces: $(2 \times 3) + (2 \times 5) + (3 \times 5) = 6 + 10 + 15 = 31$.
* Multiply by 2: $31 \times 2 = 62$. So, $62\text{ cm}^2$.

2. Second Shape
* Dimensions: $9\text{ cm}$, $3\text{ cm}$, $2\text{ cm}$
* Volume: $9 \times 3 \times 2 = 54$. So, $54\text{ cm}^3$.
* Surface Area:
* Faces: $(9 \times 3) + (9 \times 2) + (3 \times 2) = 27 + 18 + 6 = 51$.
* Multiply by 2: $51 \times 2 = 102$. So, $102\text{ cm}^2$.

3. Third Shape
* Dimensions: $4\text{ m}$, $4\text{ m}$, $12\text{ m}$
* Volume: $4 \times 4 \times 12 = 16 \times 12 = 192$. So, $192\text{ m}^3$.
* Surface Area:
* Faces: $(4 \times 4) + (4 \times 12) + (4 \times 12) = 16 + 48 + 48 = 112$.
* Multiply by 2: $112 \times 2 = 224$. So, $224\text{ m}^2$.

4. Fourth Shape
* Dimensions: $110\text{ mm}$, $20\text{ mm}$, $70\text{ mm}$
* Volume: $110 \times 20 \times 70 = 2200 \times 70 = 154,000$. So, $154,000\text{ mm}^3$.
* Surface Area:
* Faces: $(110 \times 20) + (110 \times 70) + (20 \times 70) = 2200 + 7700 + 1400 = 11,300$.
* Multiply by 2: $11,300 \times 2 = 22,600$. So, $22,600\text{ mm}^2$.

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Section B: Cubes

5. Fifth Shape (First Cube)
* Side length: $6\text{ cm}$
* Volume: $6 \times 6 \times 6 = 216$. So, $216\text{ cm}^3$.
* Surface Area: One face is $6 \times 6 = 36$. There are 6 faces. $36 \times 6 = 216$. So, $216\text{ cm}^2$.

6. Sixth Shape (Second Cube)
* Side length: $30\text{ mm}$
* Volume: $30 \times 30 \times 30 = 27,000$. So, $27,000\text{ mm}^3$.
* Surface Area: One face is $30 \times 30 = 900$. Six faces: $900 \times 6 = 5,400$. So, $5,400\text{ mm}^2$.

7. Seventh Shape (Third Cube)
* Side length: $8\text{ m}$
* Volume: $8 \times 8 \times 8 = 512$. So, $512\text{ m}^3$.
* Surface Area: One face is $8 \times 8 = 64$. Six faces: $64 \times 6 = 384$. So, $384\text{ m}^2$.

8. Eighth Shape (Fourth Cube)
* Side length: $5\text{ cm}$
* Volume: $5 \times 5 \times 5 = 125$. So, $125\text{ cm}^3$.
* Surface Area: One face is $5 \times 5 = 25$. Six faces: $25 \times 6 = 150$. So, $150\text{ cm}^2$.

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: $150\text{ cm}^2$