Surface area and nets, step by step
Surface area is the same box as volume, asked the other way round: not how much fills it, but how much wraps it.
The question
cm²
Surface area of a 7 × 10 × 13 box
7 × 10 × 13 cm
front and back:2 × 7 × 13 =182
front and back:2 × 7 × 13 =182
the two sides:2 × 10 × 13 =260
front and back:2 × 7 × 13 =182
the two sides:2 × 10 × 13 =260
top and bottom:2 × 7 × 10 =140
front and back:2 × 7 × 13 =182
the two sides:2 × 10 × 13 =260
top and bottom:2 × 7 × 10 =140
total:582
- Six faces, and the drawing can only show you three of them. The three you cannot see are the reason the usual wrong answer here is five faces added perfectly.
- Front and back are 7 by 13, and they are identical — so that pair is 2 × 7 × 13 = 182.
- The two sides are 10 by 13, and they are identical — so that pair is 2 × 10 × 13 = 260.
- Top and bottom are 7 by 10, and they are identical — so that pair is 2 × 7 × 10 = 140.
- Three pairs, six faces, none missed: 182 + 260 + 140 = 582 square cm.
How it works.
- 01
Six faces, and the drawing can only show you three of them. The three you cannot see are the reason the usual wrong answer here is five faces added perfectly.
- 02
Front and back are 7 by 13, and they are identical — so that pair is 2 × 7 × 13 = 182.
- 03
The two sides are 10 by 13, and they are identical — so that pair is 2 × 10 × 13 = 260.
- 04
Top and bottom are 7 by 10, and they are identical — so that pair is 2 × 7 × 10 = 140.
- 05
Three pairs, six faces, none missed: 182 + 260 + 140 = 582 square cm.