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QuestionMr. Magoo's bedroom is 15 ft by 20 ft. How many gallons of paint (covers 100 ft² each) does he need for the walls? a. 6 b. 5 c. 4 d. 3

Studdy Solution

STEP 1

Assumptions1. The room is a rectangular prism with dimensions15ft by20ft. . We are only painting the walls of the room, not the floor or ceiling.
3. Each gallon of paint covers100 square feet.
4. We are looking for the minimum number of whole gallons needed, as paint is typically sold in whole gallons.

STEP 2

First, we need to find the total area of the walls. Since we are only painting the walls, we can ignore the floor and ceiling. The walls of a rectangular room form a rectangular prism, so the total area of the walls is the perimeter of the base times the height.
Area=2×(Length+Width)×HeightArea =2 \times (Length + Width) \times Height

STEP 3

Now, plug in the given values for the length, width, and height to calculate the area.
Area=2×(15 ft+20 ft)×8 ftArea =2 \times (15\,ft +20\,ft) \times8\,ft

STEP 4

Calculate the total area of the walls.
Area=2×(35 ft)×8 ft=560 ft2Area =2 \times (35\,ft) \times8\,ft =560\,ft^{2}

STEP 5

Now that we have the total area of the walls, we can find out how many gallons of paint Mr. Magoo will need. We do this by dividing the total area by the area that one gallon of paint can cover.
Gallons of paint=Total area/Area covered by one gallonGallons\, of\, paint = Total\, area / Area\, covered\, by\, one\, gallon

STEP 6

Plug in the values for the total area and the area covered by one gallon to calculate the gallons of paint.
Gallons of paint=560 ft2/100 ft2Gallons\, of\, paint =560\,ft^{2} /100\,ft^{2}

STEP 7

Calculate the gallons of paint needed.
Gallons of paint=560 ft2/100 ft2=5.6Gallons\, of\, paint =560\,ft^{2} /100\,ft^{2} =5.6

STEP 8

Since paint is typically sold in whole gallons, Mr. Magoo will need to buy6 gallons of paint, even though he will not use all of the sixth gallon. So, the answer is (a)6.
Mr. Magoo needs to buy6 gallons of paint.

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