Question #67f43

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Answer 1 · 2017-12-21T14:09:12

$1 m^{3}$ $1m^3$

convert both units into metres:

$1 m = 100 c m \to 1 m^{2} = (100^{2}) c m^{2} = 10^{4} c m^{2}$ $1m = 100 cm -> 1m^2 = (100^2)cm^2 = 10^4 cm^2$

$10^{12} c m^{2} = \frac{10^{12}}{10^{4}} m^{2} = 10^{8} m^{2}$ $10^12 cm^2 = (10^12)/(10^4) m^2 = 10^8 m^2$

$2.0 \cdot 10^{12} c m^{2} = 2.0 \cdot 10^{8} m^{2}$ $2.0 * 10^12 cm^2 = 2.0 * 10^8 m^2$

$5 \cdot 10^{- 9} m = 5 \cdot 10^{- 9} m$ $5 * 10^-9m = 5 * 10^-9 m$

to find the volume (3D), multiply the area of film that the oil covers (2D) by the thickness of the oil (1D).

$V = 2.0 \cdot 10^{8} m^{2} \cdot 5 \cdot 10^{- 9} m$ $V = 2.0*10^8 m^2 * 5 * 10^-9m$

$2 \cdot 5 = 10$ $2*5 = 10$

$10^{8} \cdot 10^{- 9} = 10^{8 - 9} = 10^{- 1}$ $10^8 * 10^-9 = 10^(8-9) = 10^-1$

$2.0 \cdot 10^{8} \cdot 5 \cdot 10^{- 9} = 10 \cdot 10^{- 1}$ $2.0*10^8 * 5 * 10^-9 = 10 * 10^-1$

$10^{10} - 1 = 10^{1} \cdot 10^{- 1} = 10^{1 - 1} = 10^{0}$ $10 ^ 10-1 = 10^1 * 10^-1 = 10^(1-1) = 10^0$

$10^{0} = 1$ $10^0 = 1$

$V = 1 m^{3}$ $V = 1m^3$