To find the total surface area of the prop, we first need to find the surface area of the square prism with the vertical rectangle removed from the bottom middle.
The surface area of the square prism is 2lw + 2lh + 2wh, where l = 10 feet, w = 10 feet, and h = 3 feet.
Surface Area = 2(10)(10) + 2(10)(3) + 2(10)(3)
Surface Area = 200 + 60 + 60
Surface Area = 320 ft²
Next, we need to find the surface area of the bottom rectangle that was removed.
The surface area of the rectangle is lw, where l = 8 feet and w = 5 feet.
Surface Area = 8(5)
Surface Area = 40 ft²
Therefore, the total surface area that will need to be painted is 320 ft² - 40 ft² = 280 ft².
The closest answer choice is not listed, but the correct calculation for the total surface area is 280 ft.².
Surface Area of Composite 3D Figures Quick Check
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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
1 answer
1 answer