An open rectangular box measuring 28cm by 20cm by 12cm internally is made of wood 0.5 cm thick. find the volume of wood used in making box?

To find the volume of wood used in making the box, we need to calculate the difference between the external volume and the internal volume of the box.

1. Calculate the external volume of the box:
- Length: 28 cm
- Width: 20 cm
- Height: 12 cm

External Volume = Length * Width * Height

2. Calculate the internal volume of the box by deducting the thickness of the wood from each dimension:
- Length: 28 cm - 2 * 0.5 cm
- Width: 20 cm - 2 * 0.5 cm
- Height: 12 cm - 2 * 0.5 cm

Internal Volume = Length * Width * Height

3. Calculate the volume of wood used:

Volume of Wood = External Volume - Internal Volume

Let's calculate the values step-by-step:

Step 1: Calculate the external volume of the box
External Volume = 28 cm * 20 cm * 12 cm

Step 2: Calculate the internal volume of the box
Internal Length = 28 cm - 2 * 0.5 cm
Internal Width = 20 cm - 2 * 0.5 cm
Internal Height = 12 cm - 2 * 0.5 cm

Internal Volume = Internal Length * Internal Width * Internal Height

Step 3: Calculate the volume of wood used
Volume of Wood = External Volume - Internal Volume

Let's calculate each step:

Step 1: Calculate the external volume of the box
External Volume = 28 cm * 20 cm * 12 cm
External Volume = 6,720 cm³

Step 2: Calculate the internal volume of the box
Internal Length = 28 cm - 2 * 0.5 cm
Internal Length = 27 cm
Internal Width = 20 cm - 2 * 0.5 cm
Internal Width = 19 cm
Internal Height = 12 cm - 2 * 0.5 cm
Internal Height = 11 cm

Internal Volume = Internal Length * Internal Width * Internal Height
Internal Volume = 27 cm * 19 cm * 11 cm
Internal Volume = 6,951 cm³

Step 3: Calculate the volume of wood used
Volume of Wood = External Volume - Internal Volume
Volume of Wood = 6,720 cm³ - 6,951 cm³
Volume of Wood = -231 cm³

The volume of wood used in making the box is -231 cm³. However, it is not possible to have a negative volume, so it seems there may be an error in the given dimensions or calculations. Please double-check the measurements provided.

To find the volume of wood used in making the box, we need to calculate the difference between the volume of the outer box (including the wood thickness) and the volume of the inner box.

First, let's calculate the volume of the outer box:
The length of the outer box is equal to the length of the inner box plus twice the wood thickness on each side.
So, the length of the outer box = 28cm + 2(0.5cm) + 2(0.5cm) = 29cm.

Similarly, we can calculate the width and height of the outer box:
Width of the outer box = 20cm + 2(0.5cm) + 2(0.5cm) = 21cm.
Height of the outer box = 12cm + 0.5cm + 0.5cm = 13cm.

Now, let's calculate the volume of the outer box:
Volume of the outer box = Length × Width × Height
= 29cm × 21cm × 13cm.

The next step is to find the volume of the inner box, which is the original dimensions before adding the wood thickness:
Volume of the inner box = Length × Width × Height
= 28cm × 20cm × 12cm.

Finally, subtract the volume of the inner box from the volume of the outer box to find the volume of the wood used:
Volume of the wood = Volume of the outer box - Volume of the inner box.

subtract the inside volume from the outside volume:

(29)(21)(13) - (28)(20)(12) = ?