Volume of a rectangular prism, step by step
Volume is the third dimension arriving, and the figure has to show it or a child will multiply two numbers and stop.
The question
cm³
Volume of a 9 × 7 × 9 stepped solid
9 × 7 × 9with a step on top
slab:9 × 7 × 9 =567
block:5 × 7 × 8 =280
slab:567
block:280
567 + 280 =847 cubic cm
filled box:9 × 7 × 17 =1071
notch:4 × 7 × 8 =224
filled box:1071
notch:224
1071 − 224 =847 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 9 × 7 × 9 = 567, and the block standing on it is 5 × 7 × 8 = 280.
- 567 + 280 = 847 cubic cm.
- Second way: fill the notch in to make one big box. That box is 9 × 7 × 17 = 1071, and the notch taken back off is 4 × 7 × 8 = 224.
- 1071 − 224 = 847 cubic cm. Two methods agreeing is how you know.
How it works.
- 01
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.
- 02
First way: cut it into the two boxes it already is. The slab underneath is 9 × 7 × 9 = 567, and the block standing on it is 5 × 7 × 8 = 280.
- 03
567 + 280 = 847 cubic cm.
- 04
Second way: fill the notch in to make one big box. That box is 9 × 7 × 17 = 1071, and the notch taken back off is 4 × 7 × 8 = 224.
- 05
1071 − 224 = 847 cubic cm. Two methods agreeing is how you know.