Question

How many liters of paint must you buy to paint the walls of a rectangular prism-shaped room that is 20 m by 10 m with a ceiling height of 8 m if 1 L of paint covers40 m2? (Assume there are no doors or windows and paint comes in 1-L cans.)

Answer 1

17 Liters

Step-by-step explanation

Step 1

find the total area to paint

we need to assume the floor wont be painted, so the total are to paint is

the are of a rectangle is gieven by:

`Area=length*width`

so, the total area will be

`\begin{gathered} total\text{ surface area=\lparen20*10\rparen+2\lparen20*8\rparen+2\lparen10*8\rparen} \\ total\text{ surface area=200+2\lparen160\rparen+2\lparen80\rparen} \\ total\text{ surface area=200+320+160} \\ total\text{ surface area=680 m}^2 \end{gathered}`

so , the area to paint is 680 square meters

Step 2

finally, to know the number of Liters need , divide the amount ( total area) by the rate of the paitn, so

`\begin{gathered} paint\text{ needed=}\frac{total\text{ area}}{rate\text{ paint}} \\ paint\text{ needed=}(680m^2)/(40(m^2)/(L))=17Liters \end{gathered}`

so, the total paint needes is 17 Liters, and paint comes in 1-L cans, so

`\begin{gathered} 17\text{ Liters} \\ 17\text{L}\imaginaryI\text{ters\lparen}\frac{1\text{ Can}}{1\text{ L}})=17cans \end{gathered}`

therefore, the answer is

17 Liters

I hope this helps you