Question Background
You want to paint a room. You assume no doors and windows and that your paint will go on "perfectly." At the store you realize that your paint can only be purchased in gallon cans at $43.50 per gallon and that your paint has a density of 1.23g/mL ( from information posted on the manufacturer’s web site).
Question:
a) If your room is 10' X15' X 8' and you put 0.1mm of paint on the walls, how much paint do you need?
b) After you start painting you realize that your walls are so heavily textured that it has 60% more surface area that you calculated. Do you have enough paint and if not how much more will you need... actual amount and cans of paint.
c) If you realize that you have 40 sq ft of doors and windows, do you still need to purchase additional paint? Explain your answer.
d) If you spill 75 mL of paint and you realize that you have lost 100 mL of paint because it is in your brush, roller, and paint tray and so unusable, how many feet of wall coverage did you lose?
e) Does this "wastage" cause you to have to buy more paint? Explain.
0.1 mm is tiny thickness. Typo?
Well 1 gallon = 3.785 Liters = 3785 mL
and 1 meter = 3.281 feet
area of room walls = 2*10*8 + 2*15*8 = 160 + 240 = 400 ft^2
400 ft^2 * (1 meter/ 3.281 ft)^2 = 37.2 meters^2
volume to cover = 37.2 m^2 * (0.1 /1000) m = 3.72 ^ 10^-3 m^3 =3.72 mL
( note, I think that 0.1 should be like 1 mm)
Multiply by 1.6 for texture problem ----> 5.95 mL
The doors and windows reduce the area of course
I give up, the assumed paint thickness just makes the rest hopeless. A gallon would cover the house at 0.1 mm or even 0.16 mm
@ NEddie
A math problem under any other name still is a math problem. I gave up after the second "what if" scenario.
To answer these questions, we'll need to calculate the volume of paint required, consider the textured walls, account for the area of doors and windows, calculate the lost paint due to spillage, and determine if any additional paint needs to be purchased. Let's go through each question step by step:
a) To find the volume of paint needed, we first need to calculate the total surface area of the walls. The room dimensions are given as 10' X 15' X 8', so the surface area of each wall can be calculated as follows:
- Wall 1: 10' X 8' = 80 sq ft
- Wall 2: 15' X 8' = 120 sq ft
- Wall 3: 10' X 8' = 80 sq ft
- Wall 4: 15' X 8' = 120 sq ft
The total surface area of the walls is the sum of these areas: 80 + 120 + 80 + 120 = 400 sq ft.
Now, let's convert the thickness of paint from millimeters to feet. 1 millimeter = 0.00328084 feet, so 0.1 mm of paint is approximately 0.000328084 feet.
To find the volume of paint needed, we multiply the surface area (in square feet) by the thickness (in feet): 400 sq ft * 0.000328084 ft = 0.1312336 cubic ft.
Since the density of the paint is given as 1.23 g/mL, we can convert the volume of paint from cubic feet to mL: 0.1312336 ft³ * (1000 mL / 1 ft³) = 131.2336 mL.
Therefore, you need approximately 131.23 mL of paint for the walls.
b) If your walls have 60% more surface area due to heavy texture, we need to increase the original surface area calculation by 60% (or 0.6).
The adjusted surface area of the walls is 1.6 times the original surface area: 400 sq ft * 1.6 = 640 sq ft.
Following the same calculation as in part a, the volume of paint needed for the textured walls is:
640 sq ft * 0.000328084 ft = 0.210067456 cubic ft.
0.210067456 ft³ * (1000 mL / 1 ft³) = 210.067456 mL.
Therefore, you need approximately 210.07 mL of paint for the textured walls.
To determine how much more paint you need, find the difference between the initial paint quantity and the paint needed for the textured walls:
210.07 mL - 131.23 mL = 78.84 mL.
Since 1 gallon is equal to approximately 3785 mL, you will need an additional amount of paint of 78.84 mL / 3785 mL = 0.02084 gallons.
c) If you have 40 sq ft of doors and windows, subtract this area from the total surface area of the walls (640 sq ft) calculated in part b:
640 sq ft - 40 sq ft = 600 sq ft.
We have already determined that you need approximately 210.07 mL of paint for the textured walls. Since the newly calculated surface area is still covered by this quantity, you do not need to purchase additional paint.
d) To calculate the lost wall coverage due to spillage and unusable paint, we need to subtract the lost paint (in mL) from the original paint quantity.
Lost paint = spillage (75 mL) + paint in brush, roller, and paint tray (100 mL) = 175 mL.
The original paint quantity needed for the walls (as calculated in part b) was 210.07 mL. Subtracting the lost paint, we get:
210.07 mL - 175 mL = 35.07 mL.
To convert this amount to cubic feet, we will use the conversion factor of 1 milliliter (mL) = 0.0000353147 cubic feet (ft³):
35.07 mL * 0.0000353147 ft³/mL = 0.00123715 ft³.
Therefore, you lost approximately 0.00123715 cubic feet of wall coverage.
e) The lost paint due to spillage and unusable paint is already accounted for in the initial calculations and adjustments. Therefore, the lost paint does not affect the amount of paint you need to purchase.