The Correct Answer and Explanation is:
The correct answer is C) 31.
Here is a detailed explanation of how to arrive at this answer.
The problem asks for the total surface area that will be painted on a wooden box. The box has the shape of a rectangular prism with the following dimensions:
- Height (h) = 1 foot
- Width (w) = 3 feet
- Length (l) = 5 feet
Bob plans to use this box as a tabletop, which means he will paint the top surface and the four vertical sides. The bottom surface, which will rest on the floor or a base, will not be painted. To find the total painted area, we need to calculate the area of each of these five surfaces and then add them together.
First, let’s calculate the area of the top of the box. The top surface is a rectangle with dimensions corresponding to the length and width of the box.
- Area of the top = Length × Width
- Area of the top = 5 feet × 3 feet = 15 square feet.
Next, we need to calculate the area of the four sides. A rectangular box has two pairs of identical sides.
- The front and back sides: These are two identical rectangles whose dimensions are the length and the height of the box.
- Area of one front/back side = Length × Height
- Area of one front/back side = 5 feet × 1 foot = 5 square feet.
- Since there are two of these sides (front and back), their combined area is 2 × 5 square feet = 10 square feet.
- The left and right sides: These are the other two identical rectangles, and their dimensions are the width and the height of the box.
- Area of one left/right side = Width × Height
- Area of one left/right side = 3 feet × 1 foot = 3 square feet.
- Since there are two of these sides (left and right), their combined area is 2 × 3 square feet = 6 square feet.
Now, we find the total area of all four sides by adding the areas we just calculated:
- Total area of the four sides = (Area of front and back) + (Area of left and right)
- Total area of the four sides = 10 square feet + 6 square feet = 16 square feet.
Finally, to find the total painted area, we add the area of the top to the total area of the four sides.
- Total painted area = Area of the top + Total area of the four sides
- Total painted area = 15 square feet + 16 square feet = 31 square feet.
Therefore, Bob will paint a total of 31 square feet. This corresponds to option C.
