VolumeBoxes and joined boxes
Name: Date:
Find the volume of each box. All lengths are in centimeters.
1 cm³
2 cm³
3 cm³
4 cm³
5 cm³
6 cm³
Volume of a rectangular prism worksheets
Volume is the third dimension arriving, and the figure has to show it or a child will multiply two numbers and stop. These free printable worksheets draw the box in oblique projection with all three edges labeled.
If they get stuck
Volume of a rectangular prism
The answer key prints on a separate page.
What's on this sheet
The composite sheets are the standard's own next sentence rather than a variation someone invented: the volume of a solid made of two non-overlapping prisms is the sum of their volumes. It is the step that turns a formula into a method, so it sits alongside the plain boxes rather than in a separate place.
Why this sheet works
The two prisms in a composite figure share a depth. That is not a simplification for the drawing's sake — a step that is narrower front-to-back as well as shorter changes two things at once, and the addition is what is being practiced.
How this one works
Volume of a 10 × 7 × 7 stepped solid
10 × 7 × 7with a step on top
slab:10 × 7 × 7 =490
block:3 × 7 × 7 =147
slab:490
block:147
490 + 147 =637 cubic cm
filled box:10 × 7 × 14 =980
notch:7 × 7 × 7 =343
filled box:980
notch:343
980 − 343 =637 cubic cm
- 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.
- First way: cut it into the two boxes it already is. The slab underneath is 10 × 7 × 7 = 490, and the block standing on it is 3 × 7 × 7 = 147.
- 490 + 147 = 637 cubic cm.
- Second way: fill the notch in to make one big box. That box is 10 × 7 × 14 = 980, and the notch taken back off is 7 × 7 × 7 = 343.
- 980 − 343 = 637 cubic cm. Two methods agreeing is how you know.