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Volume of composite solids worksheets

Two boxes stuck together hold the sum of what each holds alone — and finding that sum is the step that turns a formula into a method. These free printable worksheets draw only composite solids, each an L or a step built from two prisms.

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Volume of composite solids
Volume of composite solids worksheet — Two prisms, edges to 10 cm, free printable with answer key

The answer key prints on a separate page.

What's on this sheet

The plain-box volume sheets mix single prisms with composites; this one is composites throughout, because the addition is the skill and a page that lets a child settle into one box at a time never trains it. Every figure here is two non-overlapping prisms, so there is a second solid to find and a sum to write every single time.

Why this sheet works

The two prisms share a depth, drawn in oblique projection so the join is visible. That is not a shortcut for the picture's sake — a step that is narrower front-to-back as well as shorter changes two measurements at once, and splitting it cleanly into two boxes is exactly what the standard is asking for. Find each box on its own, then add.

How this one works

One question from this sheet, worked through a step at a time.

Volume of a 10 × 8 × 7 stepped solid

10 × 8 × 7with a step on top
slab:10 × 8 × 7 =560
block:4 × 8 × 3 =96
slab:560
block:96
560 + 96 =656 cubic cm
filled box:10 × 8 × 10 =800
notch:6 × 8 × 3 =144
filled box:800
notch:144
800 − 144 =656 cubic cm
  1. A block standing on a slab. There is no formula for this shape — the job is to turn it into boxes, which do have one, and there is more than one way.
  2. First way: cut it into the two boxes it already is. The slab underneath is 10 × 8 × 7 = 560, and the block standing on it is 4 × 8 × 3 = 96.
  3. 560 + 96 = 656 cubic cm.
  4. Second way: fill the notch in to make one big box. That box is 10 × 8 × 10 = 800, and the notch taken back off is 6 × 8 × 3 = 144.
  5. 800 − 144 = 656 cubic cm. Two methods agreeing is how you know.

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