An open rectangular box has internal dimensions 2m long and 20cm wide and 22.5cm deep. If the box is made of wood 2.5cm thick, calculate the volume of wood in cm cube
see your earlier post. Different numbers, same method.
To calculate the volume of wood in cm³, we need to find the volume of the outer box and subtract the volume of the inner box.
1. Convert the dimensions to centimeters:
- The length of the inner box is 2m, which is equivalent to 200cm.
- The width of the inner box is 20cm.
- The depth of the inner box is 22.5cm.
2. Calculate the volume of the outer box:
- The length of the outer box is equal to the length of the inner box plus the thickness of the wood on both sides: 200cm + 2(2.5cm) = 205cm.
- The width of the outer box is equal to the width of the inner box plus the thickness of the wood on both sides: 20cm + 2(2.5cm) = 25cm.
- The depth of the outer box is equal to the depth of the inner box plus the thickness of the wood on both sides: 22.5cm + 2(2.5cm) = 27.5cm.
3. Calculate the volume of the inner box:
- Volume = Length x Width x Depth = 200cm x 20cm x 22.5cm = 90,000cm³.
4. Calculate the volume of the outer box:
- Volume = Length x Width x Depth = 205cm x 25cm x 27.5cm = 140,875cm³.
5. Calculate the volume of wood:
- Volume of wood = Volume of outer box - Volume of inner box = 140,875cm³ - 90,000cm³ = 50,875cm³.
Therefore, the volume of wood in cm³ is 50,875cm³.
To calculate the volume of wood in the box, we need to subtract the volume of the internal space from the volume of the external space.
First, let's calculate the internal volume of the box:
Length = 2m = 200cm
Width = 20cm
Depth = 22.5cm
The internal volume of the box is given by the formula:
Internal Volume = Length x Width x Depth
Substituting the given values into the formula, we have:
Internal Volume = 200cm x 20cm x 22.5cm
Next, let's calculate the external volume of the box by adding the thickness of the wood to each dimension of the internal space.
Thickness of wood = 2.5cm
External Length = Internal Length + 2 x Thickness of Wood
External Width = Internal Width + 2 x Thickness of Wood
External Depth = Internal Depth + 2 x Thickness of Wood
Substituting the values into the respective formulas, we have:
External Length = 200cm + 2 x 2.5cm
External Width = 20cm + 2 x 2.5cm
External Depth = 22.5cm + 2 x 2.5cm
Now, calculate the external volume of the box using the formula:
External Volume = External Length x External Width x External Depth
Substituting the values, we have:
External Volume = (200cm + 2 x 2.5cm) x (20cm + 2 x 2.5cm) x (22.5cm + 2 x 2.5cm)
Finally, subtract the internal volume from the external volume to get the volume of the wood:
Volume of Wood = External Volume - Internal Volume
Solving this equation will give you the volume of wood in cm³.