Problem 22 · 2018 Math Kangaroo
Stretch
Spatial & Visual Reasoning
net-folding
The diagram shows the net of a box consisting only of rectangles. How big is the volume of the box?
Show answer
Answer: C — 80 cm³
Show hints
Hint 1 of 2
Fold the net up in your head into a closed box and find its three edge lengths.
Still stuck? Show hint 2 →
Hint 2 of 2
The band of four faces wraps around the box, so its height is one edge and its total length is twice the sum of the other two edges; a tab gives the remaining edge.
Show solution
Approach: read the box edges from the folded net
- The horizontal strip of four faces wraps around the box; its height (7 cm) is one edge, and the tab sticking out adds 10 − 7 = 3 cm for another edge.
- Folding the net up gives a rectangular box, and multiplying its three edge lengths gives the volume.
- By the official key the volume is 80 cm³ (the marked lengths in this image crop did not cleanly reproduce 80, so the key letter C is kept).
Mark:
· log in to save