Answer:
The volume of the cuboid can be calculated by dividing its mass by the density of oak:
$ \text{Volume} = \frac{\text{Mass}}{\text{Density}} = \frac{80 \text{ g}}{0.67 \text{ g/cm}^3} = 119.4 \text{ cm}^3 $
The volume of a cuboid is given by the formula:
$ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} $
Since the volume is given, we can set up an equation:
$ 119.4 \text{ cm}^3 = \text{Length} \times \text{Width} \times \text{Height} $
Since the length and width are not given, we cannot solve for the height directly. However, we can assume that the length and width are equal, which is a common assumption for a cuboid. This gives:
$ 119.4 \text{ cm}^3 = \text{Length}^2 \times \text{Height} $
Now we can solve for the height:
$ \text{Height} = \frac{119.4 \text{ cm}^3}{\text{Length}^2} $
To find the height, we need to know the length and width. If we assume the length and width are equal, we can use the volume to find the length:
$ \text{Length}^2 \times \text{Height} = 119.4 \text{ cm}^3 $
$ \text{Length}^2 = \frac{119.4 \text{ cm}^3}{\text{Height}} $
$ \text{Length} = \sqrt{\frac{119.4 \text{ cm}^3}{\text{Height}}} $
Now we can substitute this into the equation for the height:
$ \text{Height} = \frac{119.4 \text{ cm}^3}{\left(\sqrt{\frac{119.4 \text{ cm}^3}{\text{Height}}}\right)^2} $
$ \text{Height} = \frac{119.4 \text{ cm}^3}{\frac{119.4 \text{ cm}^3}{\text{Height}}} $
$ \text{Height} = \text{Height} $
This is a contradiction, so we cannot solve for the height without knowing the length and width.
