A box is made of wood 5cm thick, its internal dimension are 10cm by 8cm by 11cm, what is the volume of the wood in the box
volume wood=volume outside-volume inside
= (10+2*5)(8+2*5)(11+2*5)-10*8*11
= 20*18*21-10*8*11
Man, that is thick wood.
To calculate the volume of the wood in the box, we need to subtract the volume of the internal space from the volume of the box.
The external dimensions of the box can be calculated by adding twice the thickness (5cm) to each internal dimension.
External dimensions:
Length = 10cm + 2 * 5cm = 10cm + 10cm = 20cm
Width = 8cm + 2 * 5cm = 8cm + 10cm = 18cm
Height = 11cm + 2 * 5cm = 11cm + 10cm = 21cm
Now, we can calculate the volume of the box using the external dimensions:
Volume of the box = Length * Width * Height
Volume of the box = 20cm * 18cm * 21cm
Next, we need to calculate the volume of the internal space:
Volume of the internal space = Length * Width * Height
Volume of the internal space = 10cm * 8cm * 11cm
Finally, we can calculate the volume of the wood by subtracting the volume of the internal space from the volume of the box:
Volume of the wood = Volume of the box - Volume of the internal space
Volume of the wood = (20cm * 18cm * 21cm) - (10cm * 8cm * 11cm)
Now, we can calculate the value of the expression:
Volume of the wood = 7560 cm^3 - 880 cm^3
Therefore, the volume of the wood in the box is:
Volume of the wood = 6680 cm^3
To find the volume of the wood in the box, we need to calculate the volume of the outer box and subtract the volume of the inner box.
1. Start by calculating the volume of the outer box.
The outer dimensions of the box are obtained by adding the thickness of the wood on each side to the inner dimensions.
Length of the outer box = 10cm + 2(5cm) = 20cm
Width of the outer box = 8cm + 2(5cm) = 18cm
Height of the outer box = 11cm + 2(5cm) = 21cm
Volume of the outer box = Length × Width × Height
= 20cm × 18cm × 21cm
2. Next, calculate the volume of the inner box.
The volume of the inner box is equal to the volume of the space inside the outer box.
Volume of the inner box = Length × Width × Height
= 10cm × 8cm × 11cm
3. Finally, subtract the volume of the inner box from the volume of the outer box to find the volume of the wood.
Volume of the wood = Volume of the outer box - Volume of the inner box
The volume of the wood can be calculated by substituting the given values into the formula.