Question

Given: 1 inch = 2.54 cm, 1ft = 12 in, 1kg = 2.205 lb) convert the following a) 95.0 lb/ft2 to kg/m2 b) 82.7 ft2 to cm2

Answer 1

Answer:

a) 463.75kg/m²

b) 76,830.81 cm²

Explanations:

Given the following conversion rate:

• 1 inch = 2.54 cm

,

• 1ft = 12 in

,

• 1kg = 2.205

We are to convert the following parameter;

95.0lb/ft² to kg/m²

$\frac{95lb}{1ft^2}\times\frac{1\operatorname{kg}}{2.205lb}\times\frac{1ft^2}{(144)in^2}\times\frac{1in^2}{(0.0254)^2m^2}$

This can be further simplified as:

$\begin{gathered} =\frac{95}{1}\times\frac{1\operatorname{kg}}{2.205}\times\frac{1}{144}\times\frac{1}{0.00064516m^2} \\ =\frac{95\operatorname{kg}}{0.2048512032m^2} \\ =463.75\operatorname{kg}m^{-2} \end{gathered}$

b) For the conversion:

82.7 ft² to cm²

If 1ft = 12 in

1ft² = 12²in²

1ft² = 144in²

Similarly,

If 1 inch = 2.54 cm

1in² = (2.54)²cm²

1in² = 6.4516cm²

Applying these formulas for the conversion:

$\begin{gathered} =82.7\cancel{ft^2}^{}\times\frac{144\cancel{in^2}^{}}{1\cancel{ft^2}^{}}\times\frac{6.4516\operatorname{cm}}{1\cancel{in^2}^{}} \\ =76,830.81\operatorname{cm}^2 \end{gathered}$

Hence the conversion of 82.7 ft² to cm² is 76,830.81 cm²