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
330 ft.2
330 ft. squared
370 ft.2
370 ft. squared
410 ft.2
410 ft. squared
180 ft.2
180 ft. squared
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The total surface area of the prop that will need to be painted is 370 ft^2.
To calculate the surface area, we need to find the area of each of the individual surfaces of the shape and then sum them up.
The area of the square front and back faces would be 10ft x 10ft = 100 ft^2 each, for a total of 200 ft^2.
The area of the top and bottom faces would be the same as the front and back faces since it is also a square, so they would each have an area of 100 ft^2, totaling 200 ft^2.
The area of the two rectangular sides would be 10ft x 4ft = 40 ft^2 each, for a total of 80 ft^2.
The area of the rectangular portion removed from the middle (which would be the same as the top and bottom faces) is 100 ft^2.
Adding all these areas together: 200 ft^2 (front and back) + 200 ft^2 (top and bottom) + 80 ft^2 (two sides) + 100 ft^2 (rectangular portion removed) = 580 ft^2.
Since the depth of the magnet is 3 feet, we only need to account for the areas that will need to be painted on the outside. The depth is 3 feet for all surfaces except for the front and back faces, which have a depth of 5 feet due to the portion removed from the middle.
Therefore, the total surface area that will need to be painted is 370 ft^2 (200 ft^2 front and back x 3 ft) + 100 ft^2 (top and bottom x 3 ft) + 80 ft^2 (two sides x 3 ft) + 100 ft^2 (rectangular portion x 5 ft). This equals 370 ft^2.
Use the image to answer the question.
An illustration shows a 3-dimensional line diagram of a truck that appears as two adjoining rectangular prisms placed on two visible wheels. The rectangular prism on the left, representing the cab section of the truck, has a height of 3 inches and a horizontal length of 2 inches. The rectangular prism on the right, or the cargo section, is 6 inches high. The back of the truck is marked as 3 inches deep. The total horizontal length of the two prisms combined is 11 inches.
A toy truck is comprised of a rectangular cab and a shipping container that it is carrying. What is the total surface area of the truck (excluding the wheels)?
(1 point)
Responses
228 in.2
228 in. squared
120 in.2 120 in. squared
234 in.2 234 in. squared
222 in.2
222 in. squared
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The total surface area of the truck (excluding the wheels) is 222 in^2.
To calculate the total surface area, we need to find the area of each individual surface of the two rectangular prisms (cab and cargo section) and then sum them up.
For the cab section:
- The front and back faces would have an area of 2 inches x 3 inches = 6 in^2 each, for a total of 12 in^2.
- The top and bottom faces would have an area of 2 inches x 3 inches = 6 in^2 each, for a total of 12 in^2.
- The two side faces (left and right) would have an area of 3 inches x 3 inches = 9 in^2 each, for a total of 18 in^2.
For the cargo section:
- The front and back faces would have an area of 2 inches x 6 inches = 12 in^2 each, for a total of 24 in^2.
- The top and bottom faces would have an area of 2 inches x 6 inches = 12 in^2 each, for a total of 24 in^2.
- The two side faces (left and right) would have an area of 3 inches x 6 inches = 18 in^2 each, for a total of 36 in^2.
Adding up all the areas:
12 in^2 (cab front and back) + 12 in^2 (cab top and bottom) + 18 in^2 (cab sides) + 24 in^2 (cargo front and back) + 24 in^2 (cargo top and bottom) + 36 in^2 (cargo sides) = 126 in^2 for the cab section and 96 in^2 for the cargo section.
The total surface area of the truck (excluding the wheels) would be 126 in^2 (cab) + 96 in^2 (cargo) = 222 in^2.