Question

Math
A carpenter constructed a closed wooden box with internal measurements 1.5m long 0.8m width and 1m high. wood used in constructing the box was 1cm thick and density of 0.6g/cm. Find volume of the wood used in constructing the box
2.mass of the box in kg correct to 1decimal place

Answer 1

I want an answer

Answer 2

L = Length

L = 1.5 m = 150 cm

W = Width

W = 0.8 m = 80 cm

H = Height

H = 1 m = 100 cm

Volume of the outside side of the box:

Vo = L ∙ W ∙ H = 150 ∙ 80 ∙ 100 = 1 200 000 cm³

The dimensions of the inner side are less than 1 cm thick on the right side and 1 cm thick on the left side.

So the internal dimensions are less than the external dimensions by 2 cm.

Volume of the internal side of the box:

Vi = ( L - 2 ) ∙ ( W - 2 ) ∙ ( H - 2 ) = 148 ∙ 78 ∙ 98 = 1 131 312 cm³

Volume of the wood = Volume of the outside side of the box - Volume of the internal side of the box

Ww= Vo - Vi = 1 200 000 - 1 131 312 = 68 688 cm³

1 kg = 1000 g

1 g = 1 kg / 1000

Density:

ρ = 0.6 g / cm³

ρ = ( 0.6 g / cm³ ) / 1000

ρ = 0.0006 kg / cm³

Mass of the box = Density ∙ Volume of the wood

m = 0.0006 kg / cm³ ∙ 68 688 cm³ = 28.0704 kg

m = 28.1 kg

to one decimal place

Remark:

28.0704 kg is 0.0704 kg away from 28 kg and 0.0296 kg from away 28.1 kg.

So 28.0704 kg is closer to 28.1 kg than 28 kg