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)
To calculate the volume of wood required to make the box, we need to find the difference between the external and internal dimensions of the box.
Given:
External dimensions: length = 17 cm, width = 12 cm, height = 10 cm
Wood thickness: 1 cm
To find the internal dimensions, subtract twice the wood thickness from each external dimension:
Internal length = External length - 2 * Wood thickness
Internal width = External width - 2 * Wood thickness
Internal height = External height - 2 * Wood thickness
Substituting the given values, we have:
Internal length = 17 cm - 2 * 1 cm = 17 cm - 2 cm = 15 cm
Internal width = 12 cm - 2 * 1 cm = 12 cm - 2 cm = 10 cm
Internal height = 10 cm - 2 * 1 cm = 10 cm - 2 cm = 8 cm
Now, we can find the volume of wood required by calculating the difference in volume between the external and internal dimensions.
Volume of wood = (External volume) - (Internal volume)
= (External length * External width * External height) - (Internal length * Internal width * Internal height)
= (17 cm * 12 cm * 10 cm) - (15 cm * 10 cm * 8 cm)
= 2,040 cm³ - 1,200 cm³
= 840 cm³
Therefore, 840 cm³ of wood is required to make the closed rectangular box.