How Many Gallons Of Paint Are Required To Paint The Walls Of A Building 33 Ft. Long, 31 Ft. Wide, And 47 Ft. High, If 1 Gallon Of Paint Will Cover 500

July 16, 2022

How many gallons of paint are required to paint the walls of a building 33 ft. long, 31 ft. wide, and 47 ft. high, if 1 gallon of paint will cover 500 ft² of the wall?

Answer:

12.032 gallons of paint are required to paint the walls of the building.

Step-by-step explanation:

Step 1: Write the given

Length of the room= 33 ft
Width of the room= 31 ft
Height of the room= 47 ft

Step 2: Find the surface area of the wall

The building is considered as rectangular prism, which has six faces.
The area of the six faces are as follows: two 31 ft by 33 ft "rooftop" and base, and two 33 ft by 47 ft and two 31 ft by 47 ft walls.
$surface area of wall= (2)(33 ft)(47 ft) +(2)(31 ft)(47 ft)$
$surface area of wall=6016 ft^{2}$

Step 3: Find the number of gallons necessary to paint the walls.

Use the relationship: 1 gallon of paint covers 500 square ft of wall
$Gallons of paint=surface area of wall*(\frac{gallon of paint}{surface area of wall})$
$Gallons of paint=(6016ft^{2} )*(\frac{1 gallon}{500ft^{2} })$
$Gallons of paint=12.032 gallons$