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Volume of Composite Figures - Worksheet 6 - 5th Grade

Medium

Decompose two joined rectangular prisms, multiply each set of dimensions, and add their volumes. Diagrams are not to scale.

medium: Use larger dimensions and show both volume calculations.

14 problems · 20-30 minutes · Skills: volume, addition, multiplication

About This Worksheet

This medium-level worksheet contains 14 problems designed for 5th Grade students practicing volume of composite figures. Medium worksheets introduce larger numbers and varied question formats to deepen understanding and build fluency.

Multiply whole numbers and find the volume of a rectangular prism: length × width × height.

  • Decompose two joined rectangular prisms, multiply each set of dimensions, and add their volumes. Diagrams are not to scale.
  • Add volumes, not edge lengths. Count each region once and use cubic units.

How to Solve: Worked Example

Example Problem: Two non-overlapping prisms have dimensions 4 × 3 × 5 cm and 2 × 3 × 2 cm. What is their combined volume?
Solution Steps:
  1. Left prism: 4 × 3 × 5 = 60 cubic centimeters.
  2. Right prism: 2 × 3 × 2 = 12 cubic centimeters.
  3. Add the non-overlapping parts: 60 + 12 = 72.
Answer: 72 cm³
Tip: Add volumes, not edge lengths. Count each region once and use cubic units.
1
Two prisms touch without overlapping. Left: 4 × 7 × 10 cm. Right: 8 × 7 × 6 cm. Find the total volume.
4 cm8 cm10 cm6 cmdepth 7 cm
Diagram not to scale.
2
Two prisms touch without overlapping. Left: 3 × 2 × 12 cm. Right: 9 × 2 × 4 cm. Find the total volume.
3 cm9 cm12 cm4 cmdepth 2 cm
Diagram not to scale.
3
Two prisms touch without overlapping. Left: 7 × 4 × 8 cm. Right: 8 × 4 × 4 cm. Find the total volume.
7 cm8 cm8 cm4 cmdepth 4 cm
Diagram not to scale.
4
Two prisms touch without overlapping. Left: 5 × 4 × 10 cm. Right: 7 × 4 × 2 cm. Find the total volume.
5 cm7 cm10 cm2 cmdepth 4 cm
Diagram not to scale.
5
Two prisms touch without overlapping. Left: 9 × 4 × 12 cm. Right: 9 × 4 × 5 cm. Find the total volume.
9 cm9 cm12 cm5 cmdepth 4 cm
Diagram not to scale.
6
Two prisms touch without overlapping. Left: 12 × 3 × 10 cm. Right: 6 × 3 × 3 cm. Find the total volume.
12 cm6 cm10 cm3 cmdepth 3 cm
Diagram not to scale.
7
Two prisms touch without overlapping. Left: 11 × 2 × 6 cm. Right: 9 × 2 × 2 cm. Find the total volume.
11 cm9 cm6 cm2 cmdepth 2 cm
Diagram not to scale.
8
Two prisms touch without overlapping. Left: 3 × 2 × 8 cm. Right: 7 × 2 × 3 cm. Find the total volume.
3 cm7 cm8 cm3 cmdepth 2 cm
Diagram not to scale.
9
Two prisms touch without overlapping. Left: 8 × 7 × 8 cm. Right: 5 × 7 × 2 cm. Find the total volume.
8 cm5 cm8 cm2 cmdepth 7 cm
Diagram not to scale.
10
Two prisms touch without overlapping. Left: 3 × 7 × 8 cm. Right: 5 × 7 × 2 cm. Find the total volume.
3 cm5 cm8 cm2 cmdepth 7 cm
Diagram not to scale.
11
Two prisms touch without overlapping. Left: 5 × 3 × 9 cm. Right: 4 × 3 × 2 cm. Find the total volume.
5 cm4 cm9 cm2 cmdepth 3 cm
Diagram not to scale.
12
Two prisms touch without overlapping. Left: 2 × 7 × 10 cm. Right: 3 × 7 × 6 cm. Find the total volume.
2 cm3 cm10 cm6 cmdepth 7 cm
Diagram not to scale.
13
Two prisms touch without overlapping. Left: 2 × 2 × 7 cm. Right: 3 × 2 × 3 cm. Find the total volume.
2 cm3 cm7 cm3 cmdepth 2 cm
Diagram not to scale.
14
Two prisms touch without overlapping. Left: 4 × 3 × 9 cm. Right: 7 × 3 × 6 cm. Find the total volume.
4 cm7 cm9 cm6 cmdepth 3 cm
Diagram not to scale.

Answer Key

1. 616 cm³ (280 + 336)2. 144 cm³ (72 + 72)3. 352 cm³ (224 + 128)4. 256 cm³ (200 + 56)5. 612 cm³ (432 + 180)6. 414 cm³ (360 + 54)7. 168 cm³ (132 + 36)8. 90 cm³ (48 + 42)9. 518 cm³ (448 + 70)10. 238 cm³ (168 + 70)11. 159 cm³ (135 + 24)12. 266 cm³ (140 + 126)13. 46 cm³ (28 + 18)14. 234 cm³ (108 + 126)

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What skills does this volume worksheet cover?

This worksheet focuses on volume, addition, multiplication. It is designed for 5th Grade students and provides structured practice through varied problem types with a worked example to guide students before they begin.

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How many problems are on this worksheet?

This worksheet contains 14 problems. It typically takes 20-30 minutes to complete. An answer key with all solutions is included so parents and teachers can check work quickly.