A gallon of paint can cover 800 square feet.  Determine how many gallons should be purchased to paint two coats on each wall of a room which has dimensions 16 feet by 18 feet and an 8-foot...

A gallon of paint can cover 800 square feet.  Determine how many gallons should be purchased to paint two coats on each wall of a room which has dimensions 16 feet by 18 feet and an 8-foot ceiling. 

how do I solve this problem?

Asked on by lro1979

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sciencesolve's profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

You need to imagine the room as a rectangular prism whose dimensions are the followings:

length - 18 feet

width - 16 feet

height - 8 feet

You need to evaluate the area of the walls whose measures are 18 feet x 8 feet such that:

`A_square = 18*8 = 144`  square feet

Since there exists two wall that have these dimensions, hence, you need to evaluate its areas such that:

`A_1 = 2*144 = 288`  square feet

You need to evaluate the area of the walls whose measures are 16 feet x 8 feet such that:

`A_square = 16*8 = 128 ` square feet

Since there exists two wall that have these dimensions, hence, you need to evaluate its areas such that:

`A_2 = 2*128 = 256`  square feet

You need to evaluate the area of ceiling such that:

`A_3 = 16*18 = 288`  square feet

You need to evaluate the total area you need to paint such that:

`A = A_1 + A_2 + A_3 => A = 288 + 256 + 288 = 832`  square feet

You need to paint two times the room, hence, you need to double the area you need to cover with paint such that:

`A = 2*832 = 1664`  square feet

Since two gallons of paint cover 1600 square feet, hence, you may use the following formula to evaluate how many gallons you need to cover 1664 square feet, such that:

`x = (1664*2)/1600 = 2.08`  gallons

Hence, evaluating the amount of paint, in gallons, you need to cover the room twice, under the given conditions, yields `x = 2.08`  gallons.

jeew-m's profile pic

jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted on

When you consider a room of length 18 width 16 and height 18 feet;

Area of floor `= 18*16 = 288 ft^2`

Area of ceiling `= 18*16 = 288 ft^2`

 

There are two smaller walls with height 8ft and width 16ft.

Area of smaller walls `= 2*16*8 = 256 ft^2`

 

There are two bigger walls with height 8ft and length 18ft.

Area of bigger walls `= 2*18*8 = 288 ft^2`

 

Total area to be painted `= 288+288+256 = 832 ft^2`

 

One gallon of paint cover `800 ft^2`

Gallons needed for one coat `= 832/800`

Gallons needed for to coats `= 832/800*2 = 2.08`

 

So you need 2.08 gallons for painting.

Note:

If you cannot buy 0.08 gallons (if shopkeeper doesn't give you less than 1 gallon) you should by another gallon. So it will be 3 gallons.

 

collegechristopher's profile pic

collegechristopher | Student, Undergraduate | eNotes Newbie

Posted on

First you need to find out the square footage of the walls:

Add the width of all four walls to find the total width

16 + 16 + 18 + 18 = 68 feet

Now multiply the total width by the height of the ceiling to find the square footage of all the walls

68 feet x 8 feet = 544 square feet

Next, multiply the total square feet by two (two coats of paint)

544 x 2 = 1088

If one gallon of paint can cover 800 square feet, then you will need two gallons to paint the whole room

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