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
370 ft.2
370 ft. squared
180 ft.2
180 ft. squared
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To find the total surface area of the prop that needs to be painted, we need to calculate the surface area of each individual surface and then add them all together.
1. The top surface area of the square prism: 10 feet x 10 feet = 100 ft²
2. The front surface area of the square prism: 10 feet x 4 feet = 40 ft²
3. The back surface area of the square prism: 10 feet x 4 feet = 40 ft²
4. The two side surfaces of the square prism: 5 feet x 4 feet = 20 ft²
5. The remaining two legs on the left and right side: 10 feet x 4 feet = 40 ft²
6. The bottom surface of the square prism (not including the portion removed): 10 feet x 10 feet = 100 ft²
7. The area of the removed portion: 5 feet x 4 feet = 20 ft²
Adding all the surface areas together:
100 + 40 + 40 + 20 + 40 + 100 + 20 = 360 ft²
Since the depth of the magnet is 3 feet, we have to add the bottom surface of the removed portion:
20 ft² + 3 feet x 10 feet = 20 ft² + 30 ft² = 50 ft²
Total surface area that needs to be painted:
360 ft² + 50 ft² = 410 ft²
Therefore, the correct answer is 410 ft².