A closed rectangular wooden box has external dimensions 17x12x10. If the wood is 1cm thick, calculate the volume of wood required to make it.
(All measurements are in Cm)
That would be the difference between
17x12x10 and 15x10x8 (the inner space volume).
= 840 cm^3
To calculate the volume of wood required, we need to find the volume of both the external and internal portions of the box and then subtract them.
First, let's find the volume of the external box. The external dimensions are given as 17x12x10 cm. Therefore, the volume of the external box is:
Volume of external box = Length × Width × Height
= 17 cm × 12 cm × 10 cm
Next, let's find the dimensions of the internal box. Since the wood is 1 cm thick around the entire box, we need to subtract 2 cm from the length, width, and height.
Volume of wood = Volume of external box - Volume of internal box
Volume of internal box = (Length - 2 cm) × (Width - 2 cm) × (Height - 2 cm)
= (17 cm - 2 cm) × (12 cm - 2 cm) × (10 cm - 2 cm)
Now, we have all the information we need to calculate the volume of wood required.
Volume of wood = (17 cm × 12 cm × 10 cm) - [(17 cm - 2 cm) × (12 cm - 2 cm) × (10 cm - 2 cm)]
Simplifying the equation, we get:
Volume of wood = (17 × 12 × 10) - [(15) × (10) × (8)]
= (2040) - (1200)
= 840 cm³
Therefore, the volume of wood required to make the box is 840 cm³.