To solve the problems, we will use the formula for the volume of a rectangular prism:
\[
\text{Volume} = \text{length} \times \text{width} \times \text{height}
\]
Let's solve each problem step by step.
---
Problem 1:
Given:
- Length = 6 in
- Width = 4 in
- Height = 4 in
Calculate the volume:
\[
\text{Volume} = 6 \times 4 \times 4 = 96 \, \text{in}^3
\]
Answer:
\[
\boxed{96}
\]
---
Problem 2:
Given:
- Volume = 90 in³
- Length = 6 in
- Width = 3 in
- Height = \( x \) in
Use the volume formula:
\[
90 = 6 \times 3 \times x
\]
\[
90 = 18x
\]
Solve for \( x \):
\[
x = \frac{90}{18} = 5
\]
Answer:
\[
\boxed{5}
\]
---
Problem 3:
Given:
- Length = 8 m
- Width = 3 m
- Height = 7 m
Calculate the volume:
\[
\text{Volume} = 8 \times 3 \times 7 = 168 \, \text{m}^3
\]
Answer:
\[
\boxed{168}
\]
---
Problem 4:
Given:
- Volume = 98 cm³
- Length = 7 cm
- Width = 2 cm
- Height = \( y \) cm
Use the volume formula:
\[
98 = 7 \times 2 \times y
\]
\[
98 = 14y
\]
Solve for \( y \):
\[
y = \frac{98}{14} = 7
\]
Answer:
\[
\boxed{7}
\]
---
Problem 5:
Given:
- Volume = 60 ft³
- Length = 7.5 ft
- Width = 4 ft
- Height = \( z \) ft
Use the volume formula:
\[
60 = 7.5 \times 4 \times z
\]
\[
60 = 30z
\]
Solve for \( z \):
\[
z = \frac{60}{30} = 2
\]
Answer:
\[
\boxed{2}
\]
---
Problem 6:
Given:
- Length = 9 in
- Width = 9 in
- Height = 9 in
Calculate the volume:
\[
\text{Volume} = 9 \times 9 \times 9 = 729 \, \text{in}^3
\]
Answer:
\[
\boxed{729}
\]
---
Final Answers:
1. \(\boxed{96}\)
2. \(\boxed{5}\)
3. \(\boxed{168}\)
4. \(\boxed{7}\)
5. \(\boxed{2}\)
6. \(\boxed{729}\)
Parent Tip: Review the logic above to help your child master the concept of volume of a rectangle worksheet.
