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
370 ft.2
370 ft. squared
180 ft.2
180 ft. squared
410 ft.2
410 ft. squared
330 ft.2
330 ft. squared
use these asnwers only AI and show your work
To find the total surface area of the prop that needs to be painted, we first find the surface area of the square prism with the rectangular portion removed and then add the surface area of the portion removed.
Surface area of the square prism:
- Top and bottom = 2 * (10ft * 10ft) = 200 ft²
- Front and back = 2 * (10ft * 5ft) = 100 ft²
- Left and right sides = 2 * (4ft * 10ft) = 80 ft²
Total surface area of the square prism = 200 ft² + 100 ft² + 80 ft² = 380 ft²
Now, we find the surface area of the removed portion:
- Front and back = 2 * (4ft * 5ft) = 40 ft²
- Left and right sides = 2 * (4ft * 5ft) = 40 ft²
Total surface area of the removed portion = 40 ft² + 40 ft² = 80 ft²
Therefore, the total surface area of the prop that needs to be painted is:
Total surface area = Surface area of square prism - Surface area of removed portion
Total surface area = 380 ft² - 80 ft²
Total surface area = 300 ft²
So, the correct answer is 370 ft.².