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)
Responses
180 ft.2
180 ft. squared
370 ft.2
370 ft. squared
330 ft.2
330 ft. squared
410 ft.2
410 ft. squared
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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.
1. Top and bottom faces (square faces):
2 * (10 ft * 10 ft) = 2 * 100 = 200 ft^2
2. Front and back faces (rectangular faces):
2 * (10 ft * 3 ft) = 2 * 30 = 60 ft^2
3. Left and right faces (includes the removed portion):
2 * [(10 ft * 4 ft) + (5 ft * 4 ft)] = 2 * (40 + 20) = 2 * 60 = 120 ft^2
So, the total surface area of the prop that will need to be painted is:
200 + 60 + 120 = 380 ft^2
Therefore, the closest option is 370 ft^2.