Surface Area of Composite 3D Figures Quick Check
4 of 54 of 5 Items
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)
Responses
180 ft.2
180 ft. squared
410 ft.2
410 ft. squared
330 ft.2
330 ft. squared
370 ft.2
370 ft. squared
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To find the total surface area of the prop that will need to be painted, we first need to find the surface area of the square prism and then subtract the surface area of the rectangle removed from the middle.
Surface Area of square prism = 2lw + 2lh + 2wh
= 2(10*10) + 2(10*5) + 2(10*4)
= 200 + 100 + 80
= 380 ft²
Surface Area of removed rectangle = lw
= 4*5
= 20 ft²
Total surface area = Surface Area of square prism - Surface Area of removed rectangle
= 380 ft² - 20 ft²
= 360 ft²
The correct answer is not given in the choices provided. The correct answer should be 360 ft².