Answer to Question #93588 in Geometry for Gloria

Question

A carpenter constructed a closed wooden box 1.5m long, 0.8m wide and 0.4m high. The wood used in constructing the box was 1.0cm thick and had a density of 0.6g/cubed

(a) Determine the:
(I) volume in cm cubed of the wood used in constructing the box
(ii) mass of the box in kg correct to 1 d.p

Answer 1

Let us find the volume of air inside the box. This volume is equal to volume of a parallelepiped. Each box dimension includes relative dimension of this parallelepiped and 2 thicknesses of wood, used to construct the box. (see picture 1 for understanding)

Therefore, this parallelepiped has dimensions (1.5m-2cm)x(0.8m-2cm)x(0.4m-2cm). These are equal to (148cm)x(78cm)x(38cm). The volume of air inside the box is equal to 148cm*78cm*38cm=438672 cm cubed

Volume of the whole box=(volume of air inside the box)+(volume of wood)

(Volume of the whole box)=1.5m*0.8m*0.4m=150cm*80cm*40cm=480000 cm cubed

(Volume of wood, used to construct the box) = (volume of whole box) - (volume of air inside the box)=41328 cm cubed

We assume that mass of air inside the box is negligible in comparison to mass of wood.

mass of box = (volume of wood)*(density of wood)=24796.8 g = 24.8 kg.

Answer: (i) 41328 cm cubed; (ii) 24.8 kg