Solve the problem.
-A room measures $14 \mathrm{ft}$ by $20 \mathrm{ft}$. The ceiling is $12 \mathrm{ft}$ above the floor. The door is $3 \mathrm{ft}$ by $7 \mathrm{ft}$. A gallon of paint will cover $84.2 \mathrm{ft}^{2}$. How many gallons of paint are needed to paint the room (including the ceiling and not including the door). Round your answer up to the next whole number.
A) 13 gallons
B) 23 gallons
C) 10 gallons
D) 4 gallons

Question

Quizplus · Accepted Answer

To calculate the total area to be painted, we need to find the area of the walls and the ceiling, then subtract the area of the door. The area of the four walls can be calculated as follows: 2*(14ft * 12ft) for the two longer walls and 2*(20ft * 12ft) for the two shorter walls. The area of the ceiling is 14ft * 20ft. The area of the door is 3ft * 7ft.Total area of the walls = 2*(14ft * 12ft) + 2*(20ft * 12ft) = 2*168ft^2 + 2*240ft^2 = 336ft^2 + 480ft^2 = 816ft^2.Area of the ceiling = 14ft * 20ft = 280ft^2.Area of the door = 3ft * 7ft = 21ft^2.Total area to be painted = Area of walls + Area of ceiling - Area of door = 816ft^2 + 280ft^2 - 21ft^2 = 1096ft^2 - 21ft^2 = 1075ft^2.Total gallons of paint needed = Total area to be painted / Coverage per gallon = 1075ft^2 / 84.2ft^2/gallon ≈ 12.77 gallons.Since we can't buy a fraction of a gallon, we round up to the next whole number, which is 13 gallons.

Solve the Problem 14ft14 \mathrm{ft}14ft By 20ft20 \mathrm{ft}20ft the Ceiling Is 12ft12 \mathrm{ft}12ft

Solve the Problem $14 \mathrm{ft}$ By $20 \mathrm{ft}$ the Ceiling Is $12 \mathrm{ft}$