2. About two centuries ago, Benjamin Franklin showed that one teaspoon of oil would cover the surface of about 0.50 acre of still water. The ‘acre’ is a unit of area.

Question

Calculate the thickness (in ‘nm’) of the layer of oil that is spread over the 0.50 acre area. (Given: 1 km=0.6214 mi ; 640 acres=1 mi2 ; 1 teaspoon=5.0 cm3)

Answer 1

Volume of the oil (V) = Area (A) x Thickness (T), or

T = V/A and we are looking to solve for T (thickness). We know the volume is 5.0 cm³ so need to find the area (A).

1 km = 0.6214 mi, so 1 km² = (0.6214 mi)(0.6214 mi) = 0.3861 mi²

0.5 acres x 1 mi²/640 acres x 1 km²/0.3861 mi² x 1 cm²/1x10^-10 km² = 2x10⁷ cm² = AREA (A)

Now to find the thickness (T)...

T = 5 cm³/2x10⁷ cm² =2.5x10^-7 cm. But the question asks for the thickness in nm, so we convert, knowing that 1 nm = 1x10^-9 m.

T = 2.5x10^-7 cm = 2.5x10^-9 m = 2.5 nm