The internal dimensions of a rectangular closed wooden box are 30 cm , 18 cm and 23 cm.
What space will it occupy ( in cm^3) if the wood used is 1 cm thick?
You need to add 1 cm twice to each dimension.
1 cm on the left side and 1 cm on the right side.
External dimensions will be:
30 + 2 ∙ 1 = 30 + 2 = 32 cm
18 + 2 ∙ 1 = 18 + 2 = 20 cm
23 + 2 ∙ 1 = 23 + 2 = 25 cm
External volume of box = 32 ∙ 20 ∙ 25 = 16 000 cm³
To calculate the space occupied by the wooden box, you need to find the volume of the external dimensions and then subtract the volume of the internal dimensions.
Here's how you can calculate it step by step:
1. Calculate the volume of the external dimensions:
The length (L) of the external dimensions is equal to the internal length (30 cm) plus twice the thickness of the wood (2 * 1 cm). So, L = 30 cm + 2 cm = 32 cm.
The width (W) of the external dimensions is equal to the internal width (18 cm) plus twice the thickness of the wood (2 * 1 cm). So, W = 18 cm + 2 cm = 20 cm.
The height (H) of the external dimensions is equal to the internal height (23 cm) plus twice the thickness of the wood (2 * 1 cm). So, H = 23 cm + 2 cm = 25 cm.
The volume (V) of the external dimensions can be calculated by multiplying the length, width, and height, so V = L * W * H = 32 cm * 20 cm * 25 cm = 16,000 cm³.
2. Calculate the volume of the internal dimensions:
The volume (V_int) of the internal dimensions can also be calculated by multiplying the length, width, and height, so V_int = 30 cm * 18 cm * 23 cm = 12,420 cm³.
3. Calculate the space occupied by the wooden box:
Subtract the volume of the internal dimensions from the volume of the external dimensions to find the space occupied by the wooden box:
Space occupied = V - V_int = 16,000 cm³ - 12,420 cm³ = 3,580 cm³.
Therefore, the space occupied by the wooden box, if the wood used is 1 cm thick, is 3,580 cm³.