Question

A closed box is made up of wood which is 1cm thick .The outer dimensions of the box is 5 cm × 4 cm × 7 cm. Find the volume of the wood used.

Answer 1

The volume of a box formed with outer measures 5 cm × 4 cm × 7 cm 

V₁ = l × b × h 

= 5 × 4 × 7 

∴ V₁ = 140 cm³

Inner measures 

= l – 2w, b – 2w, h – 2w 

= (5 – 2 × 1), (4 – 2 × 1), (7 – 2 × 1) 

= (5 – 2), (4 – 2), (7 – 2) 

= 3 cm, 2 cm, 5 cm 

∴ Volume of a box formed with inner measures

V₂ = (l – 2w)(b – 2w)(h – 2w) 

= 3 × 2 × 5 = 30 cm³ 

∴ The volume of wood used = V₁ – V₂ 

= 140 – 30 = 110 cm³