Question

Question: Solve these problems about lumber dimensions.

a) TO describe to a European how houses are constructed in the US, the dimensions of “Two-by-four” lumber must be converted into metric units. The thickness × width × length dimensions are 1.50 in. × 3.50 in. × 8.00 ft in the US. What are the dimensions in cm × cm × m?

b) This lumber can be used as vertical studs, which are typically placed 16.0 in. Apart. What is that distance in centimetres?

Short answer

a)The dimensions in cm × cm × m = 3.81cm × 8.89cm × 2.44m.

b) The distance in cm = 40.6cm

Step-by-step solution

Determine the conversion used in the first answer given above

1 in = 2.54 cm

1 feet = 0.3048 m

Now we have to determine the thickness, width, and length dimensions in cm×cm ×m

$\begin{array}{l}=1.50in\times 3.50in\times 8.00ft\\ =1.50in\times \left(\frac{2.54cm}{1in}\right)\times 3.50in\times \left(\frac{2.54cm}{1in}\right)\times 8.00ft\times \left(\frac{2.54cm}{1in}\right)\\ =3.81cm\times 8.89cm\times 2.4384m\end{array}$

Rounding off to 3 significant figures, the dimensions will be = 3.81 cm x 8.89 cm x 2.44 cm

Determine the conversion used in above 2nd answer.

We all know that,

1 in = 2.54 cm

16.0 in,

$\begin{array}{c}=16.0in\times \left(\frac{2.54cm}{1in}\right)\\ =40.64cm\end{array}$

So, the distance is 40.64 cm.