Volume of a rectangular prism
The question
cm³
Volume of a 9 × 7 × 9 stepped solid
How it works.
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
- 01
A block standing on a slab. Split it into boxes — 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. Both ways agree.