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
330 ft.2
330 ft. squared
370 ft.2
370 ft. squared
410 ft.2
410 ft. squared
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page 17 of 17
To find the total surface area of the prop that needs to be painted, we need to calculate the surface area of the square prism and subtract the surface area of the rectangular portion removed from the middle.
Surface area of the square prism:
2(10*10) + 2(10*3) + 2(4*10) = 200 + 60 + 80 = 340 ft²
Surface area of the portion removed:
5*4 + 5*10 = 20 + 50 = 70 ft²
Total surface area = 340 - 70 = 270 ft²
Therefore, the total surface area of the prop that will need to be painted is 270 ft².