A carpenter constructed a closed wooden box with internal measurements 1.5metres long, 0.8 metres wide and 0.4 metres high. The wood used in constructing the box was 1.0 cm thick and had a density of 0.6g/cm3. a) Determine i) Volume in cm3, of the wood used in constructing the box . ii) mass of the box, in kilograms, correct to 1 decimal place. b) Identical cylindrical tin of diameter 10cm, height 20cm with a mass of 120g each were packed in the box. Calculate the: i) Maximum number of tins that were packed. ii) total mass of the box with the tins.
a)
i) Volume of the wooden box = 1.5m x 0.8m x 0.4m = 0.48 m^3 = 480000 cm^3
Volume of the wood used = Volume of the outer box - Volume of the inner box
Volume of the inner box = (1.5-0.02)m x (0.8-0.02)m x (0.4-0.02)m = 0.478 m^3 = 478000 cm^3
Volume of the wood used = 480000 - 478000 = 2000 cm^3
ii) Mass of the wood used = Volume x Density = 2000 cm^3 x 0.6 g/cm^3 = 1200 g = 1.2 kg
b)
i) Volume of each cylinder = πr^2h = π(5cm)^2 x 20cm = 500π cm^3
Volume of the wooden box = 480000 cm^3
Maximum number of tins that can be packed = 480000 cm^3 / 500π cm^3 ≈ 305 tins
ii) Total mass of the box with the tins = Mass of the box + (Number of tins x Mass of each tin)
= 1.2 kg + (305 x 120 g) = 1.2 kg + 36.6 kg = 37.8 kg.