the external dimensions of a closed box are 8cm by 5cm by 4cm. given that the thickness of the wood of which it is made is 0.5cm, find the volume of the wood used to make it.
So the inner dimensions, which determine the volume are:
8-1 or 7 cm
4 cm
and 3 cm
volume = 7x4x3 cm^3
= 84 cm^3
volume=8*5*4 - 7*4*3
=76 CM3
To find the volume of the wood used to make the closed box, we need to calculate the volume of the outer box and subtract the volume of the inner box.
The external dimensions of the closed box are 8cm by 5cm by 4cm.
The thickness of the wood is 0.5cm.
Calculating the dimensions of the inner box:
Length = External Length - 2 * Thickness
Width = External Width - 2 * Thickness
Height = External Height - 2 * Thickness
Substituting the values:
Length = 8cm - 2 * 0.5cm = 7cm
Width = 5cm - 2 * 0.5cm = 4cm
Height = 4cm - 2 * 0.5cm = 3cm
The volume of the outer box is:
Volume_outer = Length * Width * Height
Substituting the values:
Volume_outer = 8cm * 5cm * 4cm = 160cm³
The volume of the inner box is:
Volume_inner = Length * Width * Height
Substituting the values:
Volume_inner = 7cm * 4cm * 3cm = 84cm³
The volume of the wood used is the difference between the volumes of the outer and inner boxes:
Volume_wood = Volume_outer - Volume_inner
Substituting the values:
Volume_wood = 160cm³ - 84cm³ = 76cm³
Therefore, the volume of the wood used to make the closed box is 76cm³.
To find the volume of the wood used to make the box, we need to find the volume of the outer box and subtract the volume of the inner box.
The outer box dimensions are given as 8cm by 5cm by 4cm. We need to subtract the thickness of the wood, which is 0.5cm, from each dimension to find the inner box dimensions.
The inner box dimensions will be:
Length = 8cm - 2 * 0.5cm = 7cm
Width = 5cm - 2 * 0.5cm = 4cm
Height = 4cm - 2 * 0.5cm = 3cm
Now, we can calculate the volume of the outer box using the formula:
Volume = Length * Width * Height
Volume = 8cm * 5cm * 4cm = 160cm³
Next, we calculate the volume of the inner box using the same formula:
Volume = 7cm * 4cm * 3cm = 84cm³
Finally, we subtract the volume of the inner box from the volume of the outer box to find the volume of the wood used:
Volume of wood = Volume of outer box - Volume of inner box
Volume of wood = 160cm³ - 84cm³ = 76cm³
Therefore, the volume of the wood used to make the closed box is 76cm³.