Volume of Rectangular Prisms and Cubes With Fractions | Worksheet ... - Free Printable

Problem: Calculate the volume of each rectangular prism or cube using the formula for volume:

\[ \text{Volume} = \text{length} \times \text{width} \times \text{height} \]

The dimensions are given in fractions or mixed numbers. We will calculate the volume for each shape step by step.

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#### Shape 1:
- Dimensions: \( 5 \, \text{in} \), \( 4 \, \text{in} \), \( \frac{3}{4} \, \text{in} \)
- Volume:
\[
\text{Volume} = 5 \times 4 \times \frac{3}{4}
\]
First, multiply \( 5 \times 4 \):
\[
5 \times 4 = 20
\]
Next, multiply \( 20 \times \frac{3}{4} \):
\[
20 \times \frac{3}{4} = \frac{20 \times 3}{4} = \frac{60}{4} = 15
\]
So, the volume is:
\[
\boxed{15 \, \text{in}^3}
\]

---

#### Shape 2:
- Dimensions: \( \frac{1}{3} \, \text{yd} \), \( \frac{1}{3} \, \text{yd} \), \( \frac{1}{3} \, \text{yd} \)
- Volume:
\[
\text{Volume} = \frac{1}{3} \times \frac{1}{3} \times \frac{1}{3}
\]
Multiply the fractions:
\[
\frac{1}{3} \times \frac{1}{3} = \frac{1 \times 1}{3 \times 3} = \frac{1}{9}
\]
\[
\frac{1}{9} \times \frac{1}{3} = \frac{1 \times 1}{9 \times 3} = \frac{1}{27}
\]
So, the volume is:
\[
\boxed{\frac{1}{27} \, \text{yd}^3}
\]

---

#### Shape 3:
- Dimensions: \( 2 \, \text{in} \), \( \frac{3}{4} \, \text{in} \), \( \frac{3}{4} \, \text{in} \)
- Volume:
\[
\text{Volume} = 2 \times \frac{3}{4} \times \frac{3}{4}
\]
First, multiply \( 2 \times \frac{3}{4} \):
\[
2 \times \frac{3}{4} = \frac{2 \times 3}{4} = \frac{6}{4} = \frac{3}{2}
\]
Next, multiply \( \frac{3}{2} \times \frac{3}{4} \):
\[
\frac{3}{2} \times \frac{3}{4} = \frac{3 \times 3}{2 \times 4} = \frac{9}{8}
\]
So, the volume is:
\[
\boxed{\frac{9}{8} \, \text{in}^3}
\]

---

#### Shape 4:
- Dimensions: \( 6 \, \text{ft} \), \( \frac{2}{3} \, \text{ft} \), \( \frac{2}{3} \, \text{ft} \)
- Volume:
\[
\text{Volume} = 6 \times \frac{2}{3} \times \frac{2}{3}
\]
First, multiply \( 6 \times \frac{2}{3} \):
\[
6 \times \frac{2}{3} = \frac{6 \times 2}{3} = \frac{12}{3} = 4
\]
Next, multiply \( 4 \times \frac{2}{3} \):
\[
4 \times \frac{2}{3} = \frac{4 \times 2}{3} = \frac{8}{3}
\]
So, the volume is:
\[
\boxed{\frac{8}{3} \, \text{ft}^3}
\]

---

#### Shape 5:
- Dimensions: \( 4 \, \text{ft} \), \( \frac{3}{4} \, \text{ft} \), \( \frac{3}{4} \, \text{ft} \)
- Volume:
\[
\text{Volume} = 4 \times \frac{3}{4} \times \frac{3}{4}
\]
First, multiply \( 4 \times \frac{3}{4} \):
\[
4 \times \frac{3}{4} = \frac{4 \times 3}{4} = \frac{12}{4} = 3
\]
Next, multiply \( 3 \times \frac{3}{4} \):
\[
3 \times \frac{3}{4} = \frac{3 \times 3}{4} = \frac{9}{4}
\]
So, the volume is:
\[
\boxed{\frac{9}{4} \, \text{ft}^3}
\]

---

#### Shape 6:
- Dimensions: \( \frac{11}{12} \, \text{m} \), \( \frac{1}{2} \, \text{m} \), \( \frac{1}{2} \, \text{m} \)
- Volume:
\[
\text{Volume} = \frac{11}{12} \times \frac{1}{2} \times \frac{1}{2}
\]
First, multiply \( \frac{11}{12} \times \frac{1}{2} \):
\[
\frac{11}{12} \times \frac{1}{2} = \frac{11 \times 1}{12 \times 2} = \frac{11}{24}
\]
Next, multiply \( \frac{11}{24} \times \frac{1}{2} \):
\[
\frac{11}{24} \times \frac{1}{2} = \frac{11 \times 1}{24 \times 2} = \frac{11}{48}
\]
So, the volume is:
\[
\boxed{\frac{11}{48} \, \text{m}^3}
\]

---

#### Shape 7:
- Dimensions: \( 3 \, \text{m} \), \( 3 \, \text{m} \), \( \frac{7}{10} \, \text{m} \)
- Volume:
\[
\text{Volume} = 3 \times 3 \times \frac{7}{10}
\]
First, multiply \( 3 \times 3 \):
\[
3 \times 3 = 9
\]
Next, multiply \( 9 \times \frac{7}{10} \):
\[
9 \times \frac{7}{10} = \frac{9 \times 7}{10} = \frac{63}{10}
\]
So, the volume is:
\[
\boxed{\frac{63}{10} \, \text{m}^3}
\]

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Final Answers:

1. \( \boxed{15 \, \text{in}^3} \)
2. \( \boxed{\frac{1}{27} \, \text{yd}^3} \)
3. \( \boxed{\frac{9}{8} \, \text{in}^3} \)
4. \( \boxed{\frac{8}{3} \, \text{ft}^3} \)
5. \( \boxed{\frac{9}{4} \, \text{ft}^3} \)
6. \( \boxed{\frac{11}{48} \, \text{m}^3} \)
7. \( \boxed{\frac{63}{10} \, \text{m}^3} \)