Grade 5 Geometry Worksheet: Calculating Volume and Surface Area of Rectangular Prisms

Problem Overview:

The task involves calculating the volume and surface area of rectangular prisms (also known as cuboids) for four different shapes. The formulas for these calculations are:

1. Volume of a Rectangular Prism:
\[
V = \text{length} \times \text{width} \times \text{height}
\]

2. Surface Area of a Rectangular Prism:
\[
SA = 2 \times (\text{length} \times \text{width} + \text{width} \times \text{height} + \text{height} \times \text{length})
\]

Let's solve each problem step by step.

---

Problem 1:

- Dimensions:
- Length (\( l \)) = 3 in
- Width (\( w \)) = 3 in
- Height (\( h \)) = 2 in

#### Step 1: Calculate the Volume
\[
V = l \times w \times h = 3 \times 3 \times 2 = 18 \, \text{cubic inches}
\]

#### Step 2: Calculate the Surface Area
\[
SA = 2 \times (l \times w + w \times h + h \times l)
\]
Substitute the values:
\[
SA = 2 \times (3 \times 3 + 3 \times 2 + 2 \times 3)
\]
\[
SA = 2 \times (9 + 6 + 6)
\]
\[
SA = 2 \times 21 = 42 \, \text{square inches}
\]

#### Final Answer for Problem 1:
\[
\boxed{18 \, \text{cubic inches}, 42 \, \text{square inches}}
\]

---

Problem 2:

- Dimensions:
- Length (\( l \)) = 4 in
- Width (\( w \)) = 4 in
- Height (\( h \)) = 4 in

This is a cube (a special case of a rectangular prism where all sides are equal).

#### Step 1: Calculate the Volume
\[
V = l \times w \times h = 4 \times 4 \times 4 = 64 \, \text{cubic inches}
\]

#### Step 2: Calculate the Surface Area
For a cube, the surface area formula simplifies to:
\[
SA = 6 \times (\text{side length})^2
\]
Substitute the side length:
\[
SA = 6 \times 4^2 = 6 \times 16 = 96 \, \text{square inches}
\]

#### Final Answer for Problem 2:
\[
\boxed{64 \, \text{cubic inches}, 96 \, \text{square inches}}
\]

---

Problem 3:

- Dimensions:
- Length (\( l \)) = 9 in
- Width (\( w \)) = 5 in
- Height (\( h \)) = 6 in

#### Step 1: Calculate the Volume
\[
V = l \times w \times h = 9 \times 5 \times 6 = 270 \, \text{cubic inches}
\]

#### Step 2: Calculate the Surface Area
\[
SA = 2 \times (l \times w + w \times h + h \times l)
\]
Substitute the values:
\[
SA = 2 \times (9 \times 5 + 5 \times 6 + 6 \times 9)
\]
\[
SA = 2 \times (45 + 30 + 54)
\]
\[
SA = 2 \times 129 = 258 \, \text{square inches}
\]

#### Final Answer for Problem 3:
\[
\boxed{270 \, \text{cubic inches}, 258 \, \text{square inches}}
\]

---

Problem 4:

- Dimensions:
- Length (\( l \)) = 7 in
- Width (\( w \)) = 6 in
- Height (\( h \)) = 8 in

#### Step 1: Calculate the Volume
\[
V = l \times w \times h = 7 \times 6 \times 8 = 336 \, \text{cubic inches}
\]

#### Step 2: Calculate the Surface Area
\[
SA = 2 \times (l \times w + w \times h + h \times l)
\]
Substitute the values:
\[
SA = 2 \times (7 \times 6 + 6 \times 8 + 8 \times 7)
\]
\[
SA = 2 \times (42 + 48 + 56)
\]
\[
SA = 2 \times 146 = 292 \, \text{square inches}
\]

#### Final Answer for Problem 4:
\[
\boxed{336 \, \text{cubic inches}, 292 \, \text{square inches}}
\]

---

Summary of All Answers:

1. \( \boxed{18 \, \text{cubic inches}, 42 \, \text{square inches}} \)
2. \( \boxed{64 \, \text{cubic inches}, 96 \, \text{square inches}} \)
3. \( \boxed{270 \, \text{cubic inches}, 258 \, \text{square inches}} \)
4. \( \boxed{336 \, \text{cubic inches}, 292 \, \text{square inches}} \)

These are the final answers for the given problems. Each step was calculated using the appropriate formulas for volume and surface area of rectangular prisms.