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
410 ft.2
410 ft. squared
330 ft.2
330 ft. squared
180 ft.2
180 ft. squared
370 ft.2
To find the total surface area of the prop that needs to be painted, calculate the surface area of the square prism and subtract the surface area of the rectangular portion removed from the middle.
Surface area of square prism = 2lw + 2lh + 2wh
= 2(10*10) + 2(10*5) + 2(4*10)
= 200 + 100 + 80
= 380 ft^2
Total surface area of prop = Surface area of square prism - surface area of rectangular portion
= 380 - (5*4 + 5*10)
= 380 - 50
= 330 ft^2
The total surface area of the prop that will need to be painted is 330 ft^2.