Minnie is painting her wall-in closet. Each gallon of paint covers 275 square feet.The closet is in the shape of a right rectangular prism. The floor is 9 feet wide and 7 feet long. The ceiling is 8 feet high. How many gallons of paint should Minnie buy to cover the four walls and the ceiling with "two" coats of paint? How many gallons of paint will be left over after Minnie paints the closet? Explain. (READ CAREFULLY AND ANSWER BOTH QUESTIONS PLEASE!)
Assuming that there is no door or the door is painted as part of the wall:
Ceiling = 9 by 7 = ?
Opposite walls = 2(8*7) + 2(8*9) = ?
Combine all of above and divide by 275.
Any fraction would be left over.
To find out how many gallons of paint Minnie should buy to cover the four walls and the ceiling with two coats of paint, we first need to calculate the total area of the walls and ceiling.
1. Calculate the total area of the four walls:
To find the total area of the four walls, we need to calculate the combined area of each wall individually and then add them up.
Each wall is a rectangle, and the dimensions of the rectangles are determined by the height of 8 feet and the lengths of 7 feet and 9 feet.
So, the total area of the four walls (excluding the ceiling) can be calculated as:
2 * (length * height) + 2 * (width * height)
Using the given dimensions, the calculation would be:
2 * (7 * 8) + 2 * (9 * 8) = 112 + 144 = 256 square feet
2. Calculate the area of the ceiling:
The area of a rectangle representing the ceiling can be calculated using the length and width, which are 9 feet and 7 feet, respectively.
So, the area of the ceiling is:
length * width = 9 * 7 = 63 square feet
3. Calculate the total area to be painted:
To determine the total area that needs to be painted, we add the area of the walls to the area of the ceiling:
Total area = Area of walls + Area of ceiling = 256 square feet + 63 square feet = 319 square feet
4. Calculate the total area for two coats of paint:
Since Minnie wants to apply two coats of paint, we need to double the total area:
Total area for two coats = 319 square feet * 2 = 638 square feet
Now that we know the total area to be painted is 638 square feet, and each gallon of paint covers 275 square feet, we can calculate the number of gallons of paint Minnie should buy:
Number of gallons of paint needed = Total area for two coats ÷ Coverage area per gallon
Number of gallons of paint needed = 638 square feet ÷ 275 square feet
Calculating this:
Number of gallons of paint needed = 2.32 gallons
Therefore, Minnie should buy approximately 2.32 gallons of paint. However, it's not possible to buy a fraction of a gallon, so she should buy 3 gallons of paint.
Next, let's calculate the amount of paint that will be left over after Minnie paints the closet.
To find the amount of paint left over, we need to subtract the amount of paint used from the total amount of paint bought:
Amount of paint left over = Total amount of paint bought - Amount of paint used
Using the 3 gallons of paint bought, and since we know that each gallon covers 275 square feet, we can calculate:
Amount of paint used = Number of gallons of paint needed * Coverage area per gallon
Amount of paint used = 2.32 gallons * 275 square feet/gallon
Calculating this:
Amount of paint used = 638 square feet
Amount of paint left over = 3 gallons - 638 square feet = -635 square feet
In this case, the answer is negative, which indicates that Minnie will not have enough paint to complete the second coat and some additional paint will need to be purchased to finish the job.