Volume and Surface Area worksheet for calculating the volume and surface area of rectangular prisms.

Problem Overview:

The worksheet asks us to calculate the surface area and volume of various rectangular prisms. Let's solve each problem step by step.

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Formula Recap:

1. Surface Area of a Rectangular Prism:
\[
\text{Surface Area} = 2lw + 2lh + 2wh
\]
where \( l \) is the length, \( w \) is the width, and \( h \) is the height.

2. Volume of a Rectangular Prism:
\[
\text{Volume} = l \times w \times h
\]

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Solutions:

#### 1a. Find the surface area of this rectangular prism.
- Dimensions: \( l = 7 \), \( w = 3 \), \( h = 5 \)
- Surface Area Formula:
\[
\text{Surface Area} = 2lw + 2lh + 2wh
\]
- Substituting the values:
\[
\text{Surface Area} = 2(7 \times 3) + 2(7 \times 5) + 2(3 \times 5)
\]
\[
= 2(21) + 2(35) + 2(15)
\]
\[
= 42 + 70 + 30
\]
\[
= 142
\]

Answer for 1a: \(\boxed{142}\)

#### 1b. Find the volume of this rectangular prism.
- Dimensions: \( l = 7 \), \( w = 5 \), \( h = 8 \)
- Volume Formula:
\[
\text{Volume} = l \times w \times h
\]
- Substituting the values:
\[
\text{Volume} = 7 \times 5 \times 8
\]
\[
= 35 \times 8
\]
\[
= 280
\]

Answer for 1b: \(\boxed{280}\)

#### 2a. Find the volume of this rectangular prism.
- Dimensions: \( l = 8 \), \( w = 5 \), \( h = 7 \)
- Volume Formula:
\[
\text{Volume} = l \times w \times h
\]
- Substituting the values:
\[
\text{Volume} = 8 \times 5 \times 7
\]
\[
= 40 \times 7
\]
\[
= 280
\]

Answer for 2a: \(\boxed{280}\)

#### 2b. Find the surface area of this rectangular prism.
- Dimensions: \( l = 7 \), \( w = 2 \), \( h = 8 \)
- Surface Area Formula:
\[
\text{Surface Area} = 2lw + 2lh + 2wh
\]
- Substituting the values:
\[
\text{Surface Area} = 2(7 \times 2) + 2(7 \times 8) + 2(2 \times 8)
\]
\[
= 2(14) + 2(56) + 2(16)
\]
\[
= 28 + 112 + 32
\]
\[
= 172
\]

Answer for 2b: \(\boxed{172}\)

#### 3a. Find the surface area of this rectangular prism.
- Dimensions: \( l = 4 \), \( w = 1 \), \( h = 8 \)
- Surface Area Formula:
\[
\text{Surface Area} = 2lw + 2lh + 2wh
\]
- Substituting the values:
\[
\text{Surface Area} = 2(4 \times 1) + 2(4 \times 8) + 2(1 \times 8)
\]
\[
= 2(4) + 2(32) + 2(8)
\]
\[
= 8 + 64 + 16
\]
\[
= 88
\]

Answer for 3a: \(\boxed{88}\)

#### 3b. Find the surface area of this rectangular prism.
- Dimensions: \( l = 5 \), \( w = 4 \), \( h = 1 \)
- Surface Area Formula:
\[
\text{Surface Area} = 2lw + 2lh + 2wh
\]
- Substituting the values:
\[
\text{Surface Area} = 2(5 \times 4) + 2(5 \times 1) + 2(4 \times 1)
\]
\[
= 2(20) + 2(5) + 2(4)
\]
\[
= 40 + 10 + 8
\]
\[
= 58
\]

Answer for 3b: \(\boxed{58}\)

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Final Answers:

1a: \(\boxed{142}\)
1b: \(\boxed{280}\)
2a: \(\boxed{280}\)
2b: \(\boxed{172}\)
3a: \(\boxed{88}\)
3b: \(\boxed{58}\)