Pin by Sakshi Jindal on MATH | Volume worksheets, Shapes ... - Free Printable

To solve the problem of finding the volume of each L-block, we need to break down each shape into simpler rectangular prisms and then calculate the volume of each part. The total volume is the sum of the volumes of these parts.

Formula for Volume of a Rectangular Prism:

The volume \( V \) of a rectangular prism is given by:
\[
V = \text{length} \times \text{width} \times \text{height}
\]

Step-by-Step Solution:

#### 1)
The L-block can be divided into two rectangular prisms:
- Prism 1: Dimensions are \( 12 \, \text{in} \times 8 \, \text{in} \times 3 \, \text{in} \)
- Prism 2: Dimensions are \( 6 \, \text{in} \times 3 \, \text{in} \times 3 \, \text{in} \)

Volume of Prism 1:
\[
V_1 = 12 \times 8 \times 3 = 288 \, \text{in}^3
\]

Volume of Prism 2:
\[
V_2 = 6 \times 3 \times 3 = 54 \, \text{in}^3
\]

Total Volume:
\[
V_{\text{total}} = V_1 + V_2 = 288 + 54 = 342 \, \text{in}^3
\]

#### 2)
The L-block can be divided into two rectangular prisms:
- Prism 1: Dimensions are \( 7 \, \text{ft} \times 4 \, \text{ft} \times 4 \, \text{ft} \)
- Prism 2: Dimensions are \( 3 \, \text{ft} \times 4 \, \text{ft} \times 4 \, \text{ft} \)

Volume of Prism 1:
\[
V_1 = 7 \times 4 \times 4 = 112 \, \text{ft}^3
\]

Volume of Prism 2:
\[
V_2 = 3 \times 4 \times 4 = 48 \, \text{ft}^3
\]

Total Volume:
\[
V_{\text{total}} = V_1 + V_2 = 112 + 48 = 160 \, \text{ft}^3
\]

#### 3)
The L-block can be divided into two rectangular prisms:
- Prism 1: Dimensions are \( 9 \, \text{yd} \times 3 \, \text{yd} \times 3 \, \text{yd} \)
- Prism 2: Dimensions are \( 3 \, \text{yd} \times 3 \, \text{yd} \times 3 \, \text{yd} \)

Volume of Prism 1:
\[
V_1 = 9 \times 3 \times 3 = 81 \, \text{yd}^3
\]

Volume of Prism 2:
\[
V_2 = 3 \times 3 \times 3 = 27 \, \text{yd}^3
\]

Total Volume:
\[
V_{\text{total}} = V_1 + V_2 = 81 + 27 = 108 \, \text{yd}^3
\]

#### 4)
The L-block can be divided into two rectangular prisms:
- Prism 1: Dimensions are \( 10 \, \text{ft} \times 5 \, \text{ft} \times 3 \, \text{ft} \)
- Prism 2: Dimensions are \( 4 \, \text{ft} \times 5 \, \text{ft} \times 3 \, \text{ft} \)

Volume of Prism 1:
\[
V_1 = 10 \times 5 \times 3 = 150 \, \text{ft}^3
\]

Volume of Prism 2:
\[
V_2 = 4 \times 5 \times 3 = 60 \, \text{ft}^3
\]

Total Volume:
\[
V_{\text{total}} = V_1 + V_2 = 150 + 60 = 210 \, \text{ft}^3
\]

#### 5)
The L-block can be divided into two rectangular prisms:
- Prism 1: Dimensions are \( 15 \, \text{yd} \times 5 \, \text{yd} \times 4 \, \text{yd} \)
- Prism 2: Dimensions are \( 5 \, \text{yd} \times 5 \, \text{yd} \times 4 \, \text{yd} \)

Volume of Prism 1:
\[
V_1 = 15 \times 5 \times 4 = 300 \, \text{yd}^3
\]

Volume of Prism 2:
\[
V_2 = 5 \times 5 \times 4 = 100 \, \text{yd}^3
\]

Total Volume:
\[
V_{\text{total}} = V_1 + V_2 = 300 + 100 = 400 \, \text{yd}^3
\]

#### 6)
The L-block can be divided into two rectangular prisms:
- Prism 1: Dimensions are \( 12 \, \text{in} \times 6 \, \text{in} \times 2 \, \text{in} \)
- Prism 2: Dimensions are \( 6 \, \text{in} \times 6 \, \text{in} \times 2 \, \text{in} \)

Volume of Prism 1:
\[
V_1 = 12 \times 6 \times 2 = 144 \, \text{in}^3
\]

Volume of Prism 2:
\[
V_2 = 6 \times 6 \times 2 = 72 \, \text{in}^3
\]

Total Volume:
\[
V_{\text{total}} = V_1 + V_2 = 144 + 72 = 216 \, \text{in}^3
\]

#### 7)
The L-block can be divided into two rectangular prisms:
- Prism 1: Dimensions are \( 6 \, \text{yd} \times 3 \, \text{yd} \times 2 \, \text{yd} \)
- Prism 2: Dimensions are \( 3 \, \text{yd} \times 3 \, \text{yd} \times 2 \, \text{yd} \)

Volume of Prism 1:
\[
V_1 = 6 \times 3 \times 2 = 36 \, \text{yd}^3
\]

Volume of Prism 2:
\[
V_2 = 3 \times 3 \times 2 = 18 \, \text{yd}^3
\]

Total Volume:
\[
V_{\text{total}} = V_1 + V_2 = 36 + 18 = 54 \, \text{yd}^3
\]

#### 8)
The L-block can be divided into two rectangular prisms:
- Prism 1: Dimensions are \( 12 \, \text{ft} \times 6 \, \text{ft} \times 2 \, \text{ft} \)
- Prism 2: Dimensions are \( 6 \, \text{ft} \times 6 \, \text{ft} \times 2 \, \text{ft} \)

Volume of Prism 1:
\[
V_1 = 12 \times 6 \times 2 = 144 \, \text{ft}^3
\]

Volume of Prism 2:
\[
V_2 = 6 \times 6 \times 2 = 72 \, \text{ft}^3
\]

Total Volume:
\[
V_{\text{total}} = V_1 + V_2 = 144 + 72 = 216 \, \text{ft}^3
\]

#### 9)
The L-block can be divided into two rectangular prisms:
- Prism 1: Dimensions are \( 13 \, \text{ft} \times 6 \, \text{ft} \times 4 \, \text{ft} \)
- Prism 2: Dimensions are \( 7 \, \text{ft} \times 6 \, \text{ft} \times 4 \, \text{ft} \)

Volume of Prism 1:
\[
V_1 = 13 \times 6 \times 4 = 312 \, \text{ft}^3
\]

Volume of Prism 2:
\[
V_2 = 7 \times 6 \times 4 = 168 \, \text{ft}^3
\]

Total Volume:
\[
V_{\text{total}} = V_1 + V_2 = 312 + 168 = 480 \, \text{ft}^3
\]

Final Answers:

\[
\boxed{
\begin{array}{ll}
1) & 342 \, \text{in}^3 \\
2) & 160 \, \text{ft}^3 \\
3) & 108 \, \text{yd}^3 \\
4) & 210 \, \text{ft}^3 \\
5) & 400 \, \text{yd}^3 \\
6) & 216 \, \text{in}^3 \\
7) & 54 \, \text{yd}^3 \\
8) & 216 \, \text{ft}^3 \\
9) & 480 \, \text{ft}^3 \\
\end{array}
}
\]