A closed wooden box measures externally 20 cm long, 14 cm wide and 9 cm high.…
2011
A closed wooden box measures externally 20 cm long, 14 cm wide and 9 cm high. If the thickness of the wood is 1 cm and 1 cubic cm of wood weighs 0.5 gram, find the weight of the box.
- A.
272 gram
- B.
496 gram
- C.
504 gram
- D.
534 gram
Show answer & explanation
Correct answer: C
For a hollow box made of a material of uniform thickness, the volume of material used equals the external volume of the box minus the internal (hollow) volume enclosed by the inner walls. Since the wall thickness is removed from both opposite faces of each dimension, every internal dimension equals the external dimension minus twice the thickness.
External volume of the box = 20 cm × 14 cm × 9 cm = 2520 cm3.
Each internal dimension = external dimension − 2 × thickness: internal length = 20 − 2(1) = 18 cm, internal width = 14 − 2(1) = 12 cm, internal height = 9 − 2(1) = 7 cm.
Internal (hollow) volume = 18 cm × 12 cm × 7 cm = 1512 cm3.
Volume of wood = External volume − Internal volume = 2520 cm3 − 1512 cm3 = 1008 cm3.
Weight of wood = Volume × density = 1008 cm3 × 0.5 g/cm3 = 504 g.
As an independent check, the wood volume can also be found directly from the shell-volume expansion 2t(lb + bh + hl) − 4t2(l + b + h) + 8t3, with l = 20, b = 14, h = 9, t = 1: 2(1)(280 + 126 + 180) − 4(1)(43) + 8(1) = 1172 − 172 + 8 = 1008 cm3 — the same value, confirming the weight of 504 g.