# Ariel's bedroom is 170in long, 135in wide, and 8.3 ft high. Her bedroom has two windows that measure 15 sq.ft. each and a door that measures 20 sq.ft. Ariel and her daughter, Melody, are going to paint Ariel's bedroom. It is given that 1 gallon of paint covers 150 sq.ft. How many gallons of paint are needed to paint the four walls and the ceiling of Ariel's bedroom with one coat of paint? Round your final answer to two decimals places.

Question
Decimals
Ariel's bedroom is 170in long, 135in wide, and 8.3 ft high. Her bedroom has two windows that measure 15 sq.ft. each and a door that measures 20 sq.ft. Ariel and her daughter, Melody, are going to paint Ariel's bedroom. It is given that 1 gallon of paint covers 150 sq.ft. How many gallons of paint are needed to paint the four walls and the ceiling of Ariel's bedroom with one coat of paint? Round your final answer to two decimals places.

2021-03-08
Step 1 It is given that Ariel's bedroom is 170 in long, 135 in wide, and 8.3 ft high. Her bedroom has two windows that measure 15 sq ft. each and a door that measures 20 sq ft. Step 2 It is known that 1 inch $$\displaystyle={\frac{{{1}}}{{{12}}}}$$ ft. Thus, 170 inch $$\displaystyle={\frac{{{170}}}{{{12}}}}$$ ft $$\displaystyle={14.1667}{f}{t}$$ ft 135 inch $$\displaystyle={\frac{{{135}}}{{{12}}}}$$ ft $$\displaystyle={11.25}$$ ft. Step 3 The area of the wall as given below: A=curved surface area of room -2(area of window) - area of door Step 4 Obtain the curved surface area of the room as shown below: Curved surface area of room $$\displaystyle={2}{h}{\left({l}+{b}\right)}$$
$$\displaystyle={2}{\left({8.3}\right)}{\left({14.1667}+{11.25}\right)}$$
$$\displaystyle={421.917}$$ sq ft Step 5 Obtain the area of the wall as shown below: A = curved surface area of room -2(area of window) - area of door $$\displaystyle={421.917}-{2}{\left({15}\right)}-{20}$$
$$\displaystyle={371.91722}$$ Step 6 Obtain the area of the ceiling as shown below: Curved surface area of room $$\displaystyle={l}{b}$$
$$\displaystyle={\left({14.1667}\times{11.25}\right)}$$
$$\displaystyle\approx{159.3753}$$ sq ft Step 7 Thus, the total area to be painted is $$\displaystyle{371.91722}$$ sq ft $$\displaystyle+{159.3753}$$ sq ft $$\displaystyle={531.2925}$$ sq ft. Obtain the number of gallons of paint required as shown below: Paint required $$\displaystyle={\frac{{{531.2925}}}{{{150}}}}$$
$$\displaystyle={3.54195}$$ gallons $$\displaystyle\approx{3.54}{g}{a}{l}{l}{o}{n}{s}$$

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