mrs.Ayer is painting the outside of her son's toy box =, including the top and bottom. the toy box measures 3 feet long, 1.5 feet wise, and 2 feet high. what is the total surface area she will paint?
1 9 feet^2
2 13.5 feet^2
3 22.5 feet^2
4 27 feet^2
you should visualize 3 pairs of rectangles
2(3x1.5) + 2(3x2) + 2(1.5x2)
= 27
Answers?
To find the total surface area that Mrs. Ayer will paint, we need to calculate the surface area of each side of the toy box and then sum them up.
The toy box has six sides: a top, bottom, front, back, left, and right.
The top and bottom have the same dimensions, so we will calculate the surface area of one of them and then multiply by 2.
The surface area of the top and bottom is:
Length × Width = 3 feet × 1.5 feet = 4.5 square feet
Multiplying by 2 gives us a total of 2 × 4.5 square feet = 9 square feet for the top and bottom.
The front and back sides have the same dimensions, so we will calculate the surface area of one of them and then multiply by 2.
The surface area of the front and back is:
Length × Height = 3 feet × 2 feet = 6 square feet
Multiplying by 2 gives us a total of 2 × 6 square feet = 12 square feet for the front and back.
The left and right sides also have the same dimensions, so we will calculate the surface area of one of them and then multiply by 2.
The surface area of the left and right sides is:
Width × Height = 1.5 feet × 2 feet = 3 square feet
Multiplying by 2 gives us a total of 2 × 3 square feet = 6 square feet for the left and right sides.
Now we can sum up the surface area of all six sides:
9 square feet for the top and bottom,
12 square feet for the front and back, and
6 square feet for the left and right sides.
Adding them together, we get 9 + 12 + 6 = 27 square feet.
Therefore, the total surface area that Mrs. Ayer will paint is 27 feet^2.
So, the correct answer is option 4: 27 feet^2.
To find the total surface area that Mrs. Ayer will paint, we need to calculate the area of each side and then add them together.
The toy box has six sides: the top, bottom, front, back, and two sides.
The formula to find the surface area of a rectangular prism is:
Surface Area = 2(lw + lh + wh)
Given the dimensions of the toy box:
Length (l) = 3 feet
Width (w) = 1.5 feet
Height (h) = 2 feet
Now, let's calculate the areas of each side:
- Top and bottom sides are both rectangles, each with dimensions of 3 feet by 1.5 feet, so the area of each is 3 ft × 1.5 ft = 4.5 ft^2. Since there are two of them (top and bottom), the total area for these two sides is 2 × 4.5 ft^2 = 9 ft^2.
- Front and back sides are both rectangles, each with dimensions of 3 feet by 2 feet, so the area of each is 3 ft × 2 ft = 6 ft^2. Since there are two of them (front and back), the total area for these two sides is 2 × 6 ft^2 = 12 ft^2.
- The two side faces are also rectangles, each with dimensions of 2 feet by 1.5 feet, so the area of each is 2 ft × 1.5 ft = 3 ft^2. Since there are two of them (two sides), the total area for these two sides is 2 × 3 ft^2 = 6 ft^2.
Now, add the areas of each side together:
9 ft^2 + 12 ft^2 + 6 ft^2 = 27 ft^2
Therefore, the total surface area that Mrs. Ayer will paint is 27 feet^2.
So, the correct answer is:
4) 27 feet^2.