I'll solve all four problems step by step, calculating the volume of each composite figure.
Problem 1:
This is an L-shaped prism made of two rectangular prisms.
First rectangular prism (bottom):
- Length = 8 ft
- Width = 2 ft
- Height = 2 ft
- Volume = 8 × 2 × 2 = 32 ft³
Second rectangular prism (top):
- Length = 6 ft
- Width = 2 ft
- Height = 2 ft
- Volume = 6 × 2 × 2 = 24 ft³
Total volume = 32 + 24 = 56 ft³
Problem 2:
This is an L-shaped solid made of two rectangular prisms.
First rectangular prism (left side):
- Length = 3 ft
- Width = 4 ft
- Height = 8 ft
- Volume = 3 × 4 × 8 = 96 ft³
Second rectangular prism (right side):
- Length = 3 ft
- Width = 3 ft
- Height = 6 ft
- Volume = 3 × 3 × 6 = 54 ft³
Total volume = 96 + 54 = 150 ft³
Problem 3:
This is an L-shaped solid made of two rectangular prisms.
First rectangular prism (back):
- Length = 5 m
- Width = 4 m
- Height = 4 m
- Volume = 5 × 4 × 4 = 80 m³
Second rectangular prism (front):
- Length = 3 m
- Width = 4 m
- Height = 3 m
- Volume = 3 × 4 × 3 = 36 m³
Total volume = 80 + 36 = 116 m³
Problem 4:
This is a composite figure with three rectangular prisms.
First rectangular prism (left):
- Length = 3 m
- Width = 2 m
- Height = 2 m
- Volume = 3 × 2 × 2 = 12 m³
Second rectangular prism (middle):
- Length = x m (need to find this)
- Width = 2 m
- Height = 2 m
- The total length is 10 m, so x = 10 - 3 - 2 = 5 m
- Volume = 5 × 2 × 2 = 20 m³
Third rectangular prism (right):
- Length = 2 m
- Width = 2 m
- Height = 2 m
- Volume = 2 × 2 × 2 = 8 m³
Total volume = 12 + 20 + 8 = 40 m³
Final Answer:
1. 56 ft³
2. 150 ft³
3. 116 m³
4. x = 5 m, Total volume = 40 m³
Parent Tip: Review the logic above to help your child master the concept of composite figure volume worksheet.
