Question

Use the image to answer the question.

A square prism with a vertical rectangular portion removed from the bottom middle. The side of the square prism is 10 feet. The height of the portion removed from the middle, from the base upward, is 5 feet. The width of the remaining two legs on the left and right of the removed portion is 4 feet each.

A giant model of a magnet is being built for a museum exhibit. What is the total surface area of the prop that will need to be painted if the depth of the magnet is 3 feet?

(1 point)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the total surface area of the prop that needs to be painted, we need to calculate the surface area of each individual face of the prism and then subtract the area of the rectangular portion that was removed.

The surface area of a rectangular prism can be calculated by finding the area of each individual face and adding them all together.

1. Calculate the area of the square base:
Side length = 10 feet
Area = side length * side length = 10 ft * 10 ft = 100 sq ft

2. Calculate the area of the top and bottom faces (also squares):
Area = 2 * 100 sq ft = 200 sq ft

3. Calculate the area of the front and back faces (rectangles):
Width = 4 feet
Height = 5 feet
Area = 2 * (width * height) = 2 * (4 ft * 5 ft) = 40 sq ft

4. Calculate the area of the left and right faces (rectangles):
Length = 10 feet
Height = 5 feet
Area = 2 * (length * height) = 2 * (10 ft * 5 ft) = 100 sq ft

5. Calculate the total surface area of the prism:
Total surface area = (area of base) + (area of top and bottom faces) + (area of front and back faces) + (area of left and right faces)
Total surface area = 100 sq ft + 200 sq ft + 40 sq ft + 100 sq ft = 440 sq ft

6. Since the depth of the magnet (the rectangular portion removed) is 3 feet, we need to subtract the area of this face (rectangle) from the total surface area:
Width = 4 feet
Height = 3 feet
Area = width * height = 4 ft * 3 ft = 12 sq ft

7. Subtract the area of the removed portion from the total surface area:
Total surface area to be painted = 440 sq ft - 12 sq ft = 428 sq ft

Therefore, the total surface area of the prop that will need to be painted is 428 square feet.