Problem: Calculate the volumes of rectangular prisms and solve for unknown dimensions.
The formula for the volume of a rectangular prism is:
\[
\text{Volume} = \text{length} \times \text{width} \times \text{height}
\]
Let's solve each problem step by step.
---
Problem 1:
- Dimensions: \(6 \, \text{in} \times 4 \, \text{in} \times 4 \, \text{in}\)
- Volume:
\[
\text{Volume} = 6 \times 4 \times 4 = 96 \, \text{in}^3
\]
Answer: \(96 \, \text{in}^3\)
---
Problem 2:
- Dimensions: \(6 \, \text{in} \times x \, \text{in} \times 3 \, \text{in}\)
- Given Volume: \(90 \, \text{in}^3\)
- Solve for \(x\):
\[
\text{Volume} = 6 \times x \times 3 = 90
\]
\[
18x = 90
\]
\[
x = \frac{90}{18} = 5
\]
Answer: \(x = 5 \, \text{in}\)
---
Problem 3:
- Dimensions: \(7 \, \text{m} \times 8 \, \text{m} \times 3 \, \text{m}\)
- Volume:
\[
\text{Volume} = 7 \times 8 \times 3 = 168 \, \text{m}^3
\]
Answer: \(168 \, \text{m}^3\)
---
Problem 4:
- Dimensions: \(7 \, \text{cm} \times 7 \, \text{cm} \times y \, \text{cm}\)
- Given Volume: \(98 \, \text{cm}^3\)
- Solve for \(y\):
\[
\text{Volume} = 7 \times 7 \times y = 98
\]
\[
49y = 98
\]
\[
y = \frac{98}{49} = 2
\]
Answer: \(y = 2 \, \text{cm}\)
---
Problem 5:
- Dimensions: \(4 \, \text{ft} \times 7.5 \, \text{ft} \times z \, \text{ft}\)
- Given Volume: \(60 \, \text{ft}^3\)
- Solve for \(z\):
\[
\text{Volume} = 4 \times 7.5 \times z = 60
\]
\[
30z = 60
\]
\[
z = \frac{60}{30} = 2
\]
Answer: \(z = 2 \, \text{ft}\)
---
Problem 6:
- Dimensions: \(9 \, \text{in} \times 9 \, \text{in} \times 9 \, \text{in}\)
- Volume:
\[
\text{Volume} = 9 \times 9 \times 9 = 729 \, \text{in}^3
\]
Answer: \(729 \, \text{in}^3\)
---
Final Answers:
1. \(96 \, \text{in}^3\)
2. \(x = 5 \, \text{in}\)
3. \(168 \, \text{m}^3\)
4. \(y = 2 \, \text{cm}\)
5. \(z = 2 \, \text{ft}\)
6. \(729 \, \text{in}^3\)
\[
\boxed{96, 5, 168, 2, 2, 729}
\]
Parent Tip: Review the logic above to help your child master the concept of volume of a cube worksheet pdf.
