find the volume of iron required to make an open box whose external dimensions are 36cm×25cm×16.5cm, the box being 1.5cm thick throughout. if 1cm^3 of iron weighs 8.5g. find the weight of empty box in kilogram.
just subtract the inner dimensions from the outer ones.
mass = volume * density
To find the volume of iron required, we need to calculate the difference between the volume of the external dimensions and the volume of the internal dimensions.
1. The external dimensions of the box are given as 36cm × 25cm × 16.5cm.
2. The thickness of the box is 1.5cm throughout, so we need to subtract twice the thickness from each dimension.
- Length: 36cm - (2 × 1.5cm) = 33cm
- Width: 25cm - (2 × 1.5cm) = 22cm
- Height: 16.5cm - (2 × 1.5cm) = 13.5cm
Now, we can calculate the volume of the iron required:
Volume of iron = (Length) × (Width) × (Height)
= 33cm × 22cm × 13.5cm
To find the weight of the empty box in kilograms, we need to convert the volume of the iron to grams and then divide by the weight of 1 cm³ of iron.
Since 1 cm³ of iron weighs 8.5g:
Weight of empty box = (Volume of iron) × (Weight of 1 cm³ in g)
= (33cm × 22cm × 13.5cm) × 8.5g
Finally, to convert the weight to kilograms, divide by 1000:
Weight of empty box in kg = (33cm × 22cm × 13.5cm) × 8.5g ÷ 1000
Now you can calculate the volume of iron required and the weight of the empty box.