Question

A partly full paint can has 0.67 U.S. gallons of paint left in it. (a) What is the volume of the paint in cubic meters? (b) If all the remaining paint is used to coat a wall evenly (wall area=13m^2), how thick is the layer of wet paint? Give your answer in meters.

Answer 1

a).      (0.7 gal) x (231 in³/gal) x (1 meter / 39.37 in)³ =

     =       (0.7 x 231 x 1) / (39.37³)  cubic meter

     =           0.00265  cubic meter.

b). The volume of paint used to coat the wall is

                V  =  (area of the wall) x (thickness of the paint) .

             0.00265 m³  =  (13 m²)  x  (thick)

Divide each side
by  13 m² :              Thickness  =  0.00265 m³ / 13 m²

                                               =    0.000204 meter .

                                                   (0.204 millimeter)
                                                   (0.00802 inch)
          

Answer 2

Answer:

(a) 2.536*10^{-3}[/tex] $m^{3}$

(b) $1.95*10^{-4}m$

Explanation:

(a) The conversion from cubic meter to gallon is $1m^{3} = 264.172 gal$

$0.67 gal*\frac{1m^{3} }{264.172gal} = 2.536*10^{-3}$ $m^{3}$

(b) Now to calculate the thickness of the paint

Volume = Cross sectional Area * thickness

    $2.536*10^{-3}$ $m^{3}$ = $13m^{2}$ * thickness

    thickness = $1.95*10^{-4}m$