Question

A closed rectangular box is made of wood of 1.5 cm thickness. The exterior length and breadth are respectively 78 cm and 19 cm, and the capacity of the box is 15 cubic decimeters. Calculate the exterior height of the box.

Answer 1

Let exterior height is h cm.

Then interior dimensions are 78 – 3 = 75, 19 – 3 = 16 and h – 3  ...(Subtract two thicknesses of wood)

Interior volume = 75 × 16 × (h – 3) which must = 15 cubic decimeters

= 15000 cm³  ...(1 dm = 10 cm, 1 cu dm = 10³ cm³)

15000 cm³ = 75 × 16 × (h – 3)

⇒ h – 3 = `15000/(75 xx 16)` = 12.5 cm

⇒ h = 15.5 cm