How many cubic centimeter of iron is required to construct an open box whose external dimensions are 36cm,25cm, and 16.5 cm provided the thickness of the iron is 1.5cm. If one cubic cm of iron weighs 7.5g find the weight of the box.
outside volume: 36*25*16.5 = 14850 cm^3
inside volume: (36-3)*(25-3)*(16.5-1.5) = 10890 cm^3
metal volume: 3960 cm^3
box weight: 3960*7.5 = 29700g = 29.7kg
To calculate the volume of the iron required to construct the box, we need to find the difference between the external and internal dimensions.
External Volume:
Length = 36 cm
Width = 25 cm
Height = 16.5 cm
Internal Volume:
Length = 36 cm - 2 * 1.5 cm
Width = 25 cm - 2 * 1.5 cm
Height = 16.5 cm - 2 * 1.5 cm
To find the internal volume of the box, we subtract the internal dimensions from the external dimensions.
Internal Volume:
Length = 36 cm - 3 cm
Width = 25 cm - 3 cm
Height = 16.5 cm - 3 cm
Internal Volume:
Length = 33 cm
Width = 22 cm
Height = 13.5 cm
Now, we can calculate the volume of the iron used by subtracting the internal volume from the external volume.
Volume of Iron = External Volume - Internal Volume
Volume of Iron = (36 cm * 25 cm * 16.5 cm) - (33 cm * 22 cm * 13.5 cm)
Volume of Iron = 14820 cm³ - 9759 cm³
Volume of Iron = 5061 cm³
Since we know that one cubic centimeter of iron weighs 7.5 grams, we can calculate the weight of the box.
Weight = Volume of Iron * Weight per cubic centimeter
Weight = 5061 cm³ * 7.5 g/cm³
Weight = 37,957.5 grams
Therefore, the weight of the box is 37,957.5 grams or 37.9575 kg.
To find the volume of the open box, we need to subtract the inner box from the outer box.
First, let's calculate the volume of the outer box:
Volume_outer = Length x Width x Height
Volume_outer = 36 cm x 25 cm x 16.5 cm
Next, let's calculate the volume of the inner box:
Since the thickness of the iron is 1.5 cm, we need to subtract twice the thickness from each dimension before calculating the volume.
Volume_inner = (Length - 2 x Thickness) x (Width - 2 x Thickness) x (Height - 2 x Thickness)
Volume_inner = (36 cm - 2 x 1.5 cm) x (25 cm - 2 x 1.5 cm) x (16.5 cm - 2 x 1.5 cm)
Now, let's subtract the volume of the inner box from the volume of the outer box to get the volume of the iron used:
Volume_iron = Volume_outer - Volume_inner
To find the weight of the box, we need to multiply the volume of the iron by the weight of one cubic cm of iron.
Weight = Volume_iron x Weight_per_cubic_cm
Now we can plug in the values and calculate the weight of the box:
Volume_outer = 36 cm x 25 cm x 16.5 cm
Volume_inner = (36 cm - 2 x 1.5 cm) x (25 cm - 2 x 1.5 cm) x (16.5 cm - 2 x 1.5 cm)
Weight_per_cubic_cm = 7.5 g/cm^3
Calculate the values and find the weight of the box.