Question

You need to repaint the ceiling in your house. You measure to find that you have 201,600 in^2 of ceiling to paint. When you go to the store you find that a gallon of white ceiling paint covers about 325 ft^2. How many full gallons of paint would you need to purchase in order to paint all the ceilings in your house.

Answer 1

Given that 1 gallon of paint is required to paint 325 square feet,

`1\text{ gallon of paint}\equiv325\text{ ft}^2`

The total area of the ceiling is 201600 square inches.

Convert the units as follwos,

`\begin{gathered} 144\text{ inch}^2=1\text{ ft}^2 \\ \Rightarrow201600\text{ inch}^2=(201600)/(144)=1400\text{ ft}^2 \end{gathered}`

So the area of the ceiling is 1400 square feet.

Then the amount of paint required for the ceiling is calculated as,

`\begin{gathered} 325\text{ ft}^2\equiv1\text{ gallon} \\ 1400\text{ ft}^2\equiv(1400)/(325)\approx4.3\text{ gallons} \end{gathered}`

Thus, approximately 4.3 gallons of paint is required for the complete ceiling.