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Volume of Composite Figures - Worksheet 8 - 5th Grade

Hard

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

hard: Use total volume to find the missing height of one prism.

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

About This Worksheet

This hard-level worksheet contains 18 problems designed for 5th Grade students practicing volume of composite figures. Hard worksheets feature challenging problems including multi-step questions, missing values, and real-world applications to push students further.

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
The joined solid has volume 192 cm³. Left length 4 cm; right length 2 cm; shared depth 3 cm; right height 6 cm. Find the left height.
4 cm2 cm? cm6 cmdepth 3 cm
Diagram not to scale.
2
The joined solid has volume 560 cm³. Left length 8 cm; right length 8 cm; shared depth 7 cm; right height 4 cm. Find the left height.
8 cm8 cm? cm4 cmdepth 7 cm
Diagram not to scale.
3
The joined solid has volume 312 cm³. Left length 6 cm; right length 3 cm; shared depth 4 cm; right height 4 cm. Find the left height.
6 cm3 cm? cm4 cmdepth 4 cm
Diagram not to scale.
4
The joined solid has volume 372 cm³. Left length 4 cm; right length 9 cm; shared depth 4 cm; right height 5 cm. Find the left height.
4 cm9 cm? cm5 cmdepth 4 cm
Diagram not to scale.
5
The joined solid has volume 240 cm³. Left length 2 cm; right length 2 cm; shared depth 6 cm; right height 6 cm. Find the left height.
2 cm2 cm? cm6 cmdepth 6 cm
Diagram not to scale.
6
The joined solid has volume 768 cm³. Left length 10 cm; right length 8 cm; shared depth 6 cm; right height 6 cm. Find the left height.
10 cm8 cm? cm6 cmdepth 6 cm
Diagram not to scale.
7
The joined solid has volume 48 cm³. Left length 2 cm; right length 4 cm; shared depth 2 cm; right height 3 cm. Find the left height.
2 cm4 cm? cm3 cmdepth 2 cm
Diagram not to scale.
8
The joined solid has volume 168 cm³. Left length 2 cm; right length 5 cm; shared depth 6 cm; right height 2 cm. Find the left height.
2 cm5 cm? cm2 cmdepth 6 cm
Diagram not to scale.
9
The joined solid has volume 62 cm³. Left length 2 cm; right length 3 cm; shared depth 2 cm; right height 3 cm. Find the left height.
2 cm3 cm? cm3 cmdepth 2 cm
Diagram not to scale.
10
The joined solid has volume 188 cm³. Left length 3 cm; right length 4 cm; shared depth 4 cm; right height 5 cm. Find the left height.
3 cm4 cm? cm5 cmdepth 4 cm
Diagram not to scale.
11
The joined solid has volume 273 cm³. Left length 9 cm; right length 2 cm; shared depth 3 cm; right height 5 cm. Find the left height.
9 cm2 cm? cm5 cmdepth 3 cm
Diagram not to scale.
12
The joined solid has volume 854 cm³. Left length 11 cm; right length 3 cm; shared depth 7 cm; right height 4 cm. Find the left height.
11 cm3 cm? cm4 cmdepth 7 cm
Diagram not to scale.
13
The joined solid has volume 110 cm³. Left length 5 cm; right length 4 cm; shared depth 2 cm; right height 5 cm. Find the left height.
5 cm4 cm? cm5 cmdepth 2 cm
Diagram not to scale.
14
The joined solid has volume 355 cm³. Left length 7 cm; right length 2 cm; shared depth 5 cm; right height 4 cm. Find the left height.
7 cm2 cm? cm4 cmdepth 5 cm
Diagram not to scale.
15
The joined solid has volume 156 cm³. Left length 3 cm; right length 9 cm; shared depth 2 cm; right height 5 cm. Find the left height.
3 cm9 cm? cm5 cmdepth 2 cm
Diagram not to scale.
16
The joined solid has volume 216 cm³. Left length 6 cm; right length 7 cm; shared depth 2 cm; right height 6 cm. Find the left height.
6 cm7 cm? cm6 cmdepth 2 cm
Diagram not to scale.
17
The joined solid has volume 384 cm³. Left length 12 cm; right length 3 cm; shared depth 4 cm; right height 4 cm. Find the left height.
12 cm3 cm? cm4 cmdepth 4 cm
Diagram not to scale.
18
The joined solid has volume 80 cm³. Left length 3 cm; right length 4 cm; shared depth 4 cm; right height 2 cm. Find the left height.
3 cm4 cm? cm2 cmdepth 4 cm
Diagram not to scale.

Answer Key

1. 13 cm ((192 - 36) ÷ 12)2. 6 cm ((560 - 224) ÷ 56)3. 11 cm ((312 - 48) ÷ 24)4. 12 cm ((372 - 180) ÷ 16)5. 14 cm ((240 - 72) ÷ 12)6. 8 cm ((768 - 288) ÷ 60)7. 6 cm ((48 - 24) ÷ 4)8. 9 cm ((168 - 60) ÷ 12)9. 11 cm ((62 - 18) ÷ 4)10. 9 cm ((188 - 80) ÷ 12)11. 9 cm ((273 - 30) ÷ 27)12. 10 cm ((854 - 84) ÷ 77)13. 7 cm ((110 - 40) ÷ 10)14. 9 cm ((355 - 40) ÷ 35)15. 11 cm ((156 - 90) ÷ 6)16. 11 cm ((216 - 84) ÷ 12)17. 7 cm ((384 - 48) ÷ 48)18. 4 cm ((80 - 32) ÷ 12)

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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 18 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.