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 \(\displaystyle\approx{3.54}{g}{a}{l}{l}{o}{n}{s}\)

\(\displaystyle={2}{\left({8.3}\right)}{\left({14.1667}+{11.25}\right)}\)

\(\displaystyle={421.917}\) 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 \(\displaystyle\approx{3.54}{g}{a}{l}{l}{o}{n}{s}\)