melind wants to paint the exterior lateral surface of her house. It is nine feet high and has a perimeter of 140 feet. each gallon of paint covers 300 square feet how many one gallon cans of paint does she need to buy to paint her house
Multiply: 9 x 140 = ?? (the number of square feet the paint needs to cover)
Then divide that answer by 300.
What do you get?
And remember, you need to answer in full gallons, not any partial gallons.
To find out how many one-gallon cans of paint Melind needs to buy, we need to calculate the total surface area of the exterior lateral surface of her house.
First, determine the height of the house, which is given as nine feet.
Next, let's calculate the base of the house. Since the lateral surface area is the perimeter multiplied by the height, we can use the given perimeter of 140 feet to calculate the base.
The formula for the perimeter of a rectangle is: Perimeter = 2 × (Length + Width)
In this case, we have two equal lengths and two equal widths since we are dealing with a rectangular shape. Let's assume the length is L and the width is W.
So, we can rewrite the perimeter formula as: 140 = 2 × (L + W)
Simplifying, we have: 70 = L + W
Since the length and width are equal, we can represent both as L.
Now, we can rewrite the equation as: 70 = 2L
Dividing by 2, we find: L = 35
So, the length of the house is 35 feet, and the width is also 35 feet.
The surface area of a rectangular prism is given by the formula: Surface Area = 2lw + 2lh + 2wh, where l = length, w = width, and h = height.
To find the lateral surface area, we don't need the two faces representing the top and bottom of the house, so we can use the formula: Lateral Surface Area = 2lw + 2lh.
Substituting the values we have: Lateral Surface Area = 2(35)(9) + 2(35)(9) = 2(35)(9) + 2(35)(9) = 630 + 630 = 1260 square feet.
Now, we can calculate how many one-gallon cans of paint are needed. Since each gallon covers 300 square feet, we divide the total surface area by the coverage per gallon:
Number of gallons = Lateral Surface Area / Coverage per gallon = 1260 / 300 = 4.2 gallons.
Since we can't purchase a fraction of a gallon, we need to round up to the nearest whole number. Therefore, Melind needs to buy at least 5 one-gallon cans of paint to cover the exterior lateral surface of her house.