find the volume of iron require to make an open box whose external dimensions are 36 cm * 25cm* 16.5 cm and 1.5 cm thick throughout. if 1 cm3 of iron weighs 8.5 grams, find the weight of the empty of box in kilograms..
outside: (36)(25)(16.5) = 14850.00
inside: (34.5)(23.5)(15) = 12161.25
volume of material if a closed box: 2688.75 cm^3
Next, subtract the volume of the missing top.
Finally, just multiply that by the density to find the mass
To find the volume of the iron required to make the open box, we need to calculate the volume of the external dimensions and then subtract the volume of the internal dimensions (the empty space inside the box).
1. Calculate the volume of the external dimensions:
Volume = length * width * height
Volume = 36 cm * 25 cm * 16.5 cm
2. Calculate the volume of the internal dimensions:
Since the box is 1.5 cm thick throughout, we need to subtract 3 cm (1.5 cm on each side) from each dimension.
Volume = (length - 3 cm) * (width - 3 cm) * (height - 3 cm)
3. Calculate the volume of the iron required:
Iron Volume = External Volume - Internal Volume
4. Calculate the weight of the empty box:
Weight = Iron Volume * 8.5 grams
Let's calculate the volume of the iron required and the weight of the empty box step by step:
1. Calculate the volume of the external dimensions:
Volume = 36 cm * 25 cm * 16.5 cm
Volume = 14,040 cm³
2. Calculate the volume of the internal dimensions:
Internal Volume = (36 cm - 3 cm) * (25 cm - 3 cm) * (16.5 cm - 3 cm)
Internal Volume = 33 cm * 22 cm * 13.5 cm
Internal Volume = 9,990 cm³
3. Calculate the volume of the iron required:
Iron Volume = 14,040 cm³ - 9,990 cm³
Iron Volume = 4,050 cm³
4. Calculate the weight of the empty box:
Weight = Iron Volume * 8.5 grams
Weight = 4,050 cm³ * 8.5 grams
Weight = 34,425 grams
To convert the weight from grams to kilograms:
Weight in kilograms = Weight in grams / 1000
Weight in kilograms = 34,425 grams / 1000
Weight in kilograms = 34.425 kg
Therefore, the weight of the empty box is approximately 34.425 kilograms.