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)

330 ft.2


180 ft.2


370 ft.2


410 ft.2

Answer 1

330 ft^2

Work:
- Start with the 10×10 front and back faces, each loses a 2×5 hole: each face = 100 − 10 = 90, so front+back = 180.
- Top = 10×3 = 30.
- Bottom = 10×3 − (2×3) = 30 − 6 = 24.
- Left and right sides = 2 × (10×3) = 60.
- Interior faces of the removed notch: two side faces 5×3 each (2×15 = 30) and the top of the notch 2×3 = 6, total = 36.

Total surface area = 180 + 30 + 24 + 60 + 36 = 330 ft^2.