To find the surface area of the two-tiered steps, we need to calculate the surface area of each rectangular prism separately and then add them together.
Surface area of the large rectangle prism on the bottom:
- Front and back faces: 17 in. x 6.5 in. = 110.5 in^2
- Top and bottom faces: 17 in. x 8.5 in. = 144.5 in^2
- Side faces: 6.5 in. x 8.5 in. = 55.25 in^2 x 2 = 110.5 in^2
Total surface area of the large rectangular prism = 110.5 + 144.5 + 110.5 = 365.5 in^2
Surface area of the small rectangle prism on top:
- Front and back faces: 14 in. x 6.5 in. = 91 in^2
- Top and bottom faces: 14 in. x 8.5 in. = 119 in^2
- Side faces: 6.5 in. x 8.5 in. = 55.25 in^2 x 2 = 110.5 in^2
Total surface area of the small rectangular prism = 91 + 119 + 110.5 = 320.5 in^2
Adding the surface areas of both rectangular prisms together: 365.5 in^2 + 320.5 in^2 = 686 in^2
Therefore, the surface area of the two-tiered steps is 686 in^2.
Use the image to answer the question.
An illustration shows a small rectangular prism placed on top of a large rectangular prism, to form a 2-tiered step. The edges that are not visible are marked with dashed lines. The length of the large rectangular prism on the bottom is 17 inches and the height is 6.5 inches. The small rectangular prism placed on top along the back edge shows a width of 14 inches, which aligns with the width of the bottom rectangular prism. The total height of both rectangles is 13 inches overall. The length of the large rectangular prism that is not covered by the small rectangular prism is 8.5 inches.
Find the surface area of the two-tiered steps.
(1 point)
Responses
2,320.5 in.2
2,320.5 in. squared
1,409.5 in.2
1,409.5 in. squared
1,171.5 in.2
1,171.5 in. squared
879 in.2
7 answers
remove connecting sides of the composite figure and choose one of my answers
I'm sorry for the mistake in the previous response. After removing the connecting sides of the composite figure, we are left with two rectangular prisms stacked on top of each other.
Surface area of the large rectangular prism on the bottom:
- Front and back faces: 17 in. x 6.5 in. = 110.5 in^2
- Top and bottom faces: 17 in. x 8.5 in. = 144.5 in^2
- Side faces: 6.5 in. x 8.5 in. = 55.25 in^2 x 2 = 110.5 in^2
Total surface area of the large rectangular prism = 110.5 + 144.5 + 110.5 = 365.5 in^2
Surface area of the small rectangular prism on top:
- Front and back faces: 14 in. x 6.5 in. = 91 in^2
- Top and bottom faces: 14 in. x 8.5 in. = 119 in^2
- Side faces: 6.5 in. x 8.5 in. = 55.25 in^2 x 2 = 110.5 in^2
Total surface area of the small rectangular prism = 91 + 119 + 110.5 = 320.5 in^2
Adding the surface areas of both rectangular prisms together: 365.5 in^2 + 320.5 in^2 = 686 in^2
Therefore, the correct answer should be:
1,171.5 in^2
Surface area of the large rectangular prism on the bottom:
- Front and back faces: 17 in. x 6.5 in. = 110.5 in^2
- Top and bottom faces: 17 in. x 8.5 in. = 144.5 in^2
- Side faces: 6.5 in. x 8.5 in. = 55.25 in^2 x 2 = 110.5 in^2
Total surface area of the large rectangular prism = 110.5 + 144.5 + 110.5 = 365.5 in^2
Surface area of the small rectangular prism on top:
- Front and back faces: 14 in. x 6.5 in. = 91 in^2
- Top and bottom faces: 14 in. x 8.5 in. = 119 in^2
- Side faces: 6.5 in. x 8.5 in. = 55.25 in^2 x 2 = 110.5 in^2
Total surface area of the small rectangular prism = 91 + 119 + 110.5 = 320.5 in^2
Adding the surface areas of both rectangular prisms together: 365.5 in^2 + 320.5 in^2 = 686 in^2
Therefore, the correct answer should be:
1,171.5 in^2
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
180 ft.2
180 ft. squared
410 ft.2
410 ft. squared
370 ft.2
370 ft. squared
330 ft.2
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
180 ft.2
180 ft. squared
410 ft.2
410 ft. squared
370 ft.2
370 ft. squared
330 ft.2
To find the total surface area of the prop that will need to be painted, we need to first calculate the surface area of the square prism as if the rectangular portion at the bottom were still attached, and then subtract the surface area of the removed portion.
Surface area of the square prism with the removed portion:
- Front and back faces: 10 ft. x 5 ft. = 50 ft² x 2 = 100 ft²
- Top and bottom faces: 10 ft. x 10 ft. = 100 ft² x 2 = 200 ft²
- Side faces: 10 ft. x 5 ft. = 50 ft² x 4 = 200 ft²
Total surface area of the square prism with the removed portion = 100 ft² + 200 ft² + 200 ft² = 500 ft²
Surface area of the removed portion:
- Front and back faces: 10 ft. x 3 ft. = 30 ft² x 2 = 60 ft²
- Side faces: 5 ft. x 3 ft. = 15 ft² x 2 = 30 ft²
Total surface area of the removed portion = 60 ft² + 30 ft² = 90 ft²
Subtract the surface area of the removed portion from the total surface area of the square prism:
500 ft² - 90 ft² = 410 ft²
Therefore, the total surface area of the prop that will need to be painted is 410 ft². The correct answer is:
410 ft²
Surface area of the square prism with the removed portion:
- Front and back faces: 10 ft. x 5 ft. = 50 ft² x 2 = 100 ft²
- Top and bottom faces: 10 ft. x 10 ft. = 100 ft² x 2 = 200 ft²
- Side faces: 10 ft. x 5 ft. = 50 ft² x 4 = 200 ft²
Total surface area of the square prism with the removed portion = 100 ft² + 200 ft² + 200 ft² = 500 ft²
Surface area of the removed portion:
- Front and back faces: 10 ft. x 3 ft. = 30 ft² x 2 = 60 ft²
- Side faces: 5 ft. x 3 ft. = 15 ft² x 2 = 30 ft²
Total surface area of the removed portion = 60 ft² + 30 ft² = 90 ft²
Subtract the surface area of the removed portion from the total surface area of the square prism:
500 ft² - 90 ft² = 410 ft²
Therefore, the total surface area of the prop that will need to be painted is 410 ft². The correct answer is:
410 ft²
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
222 in.2
222 in. squared
228 in.2
228 in. squared
234 in.2 234 in. squared
120 in.2
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
222 in.2
222 in. squared
228 in.2
228 in. squared
234 in.2 234 in. squared
120 in.2
To find the total surface area of the truck (excluding the wheels), we need to calculate the surface areas of the cab section and the cargo section separately and then add them together.
Surface area of the cab section (rectangular prism on the left):
- Front and back faces: 2 in. x 3 in. = 6 in² x 2 = 12 in²
- Top and bottom faces: 2 in. x 3 in. = 6 in² x 2 = 12 in²
- Side faces: 3 in. x 3 in. = 9 in² x 2 = 18 in²
Total surface area of the cab section = 12 in² + 12 in² + 18 in² = 42 in²
Surface area of the cargo section (rectangular prism on the right):
- Front and back faces: 6 in. x 3 in. = 18 in² x 2 = 36 in²
- Top and bottom faces: 6 in. x 11 in. = 66 in² x 2 = 132 in²
- Side faces: 3 in. x 11 in. = 33 in² x 2 = 66 in²
Total surface area of the cargo section = 36 in² + 132 in² + 66 in² = 234 in²
Adding the surface areas of the cab section and cargo section together: 42 in² + 234 in² = 276 in²
Therefore, the total surface area of the truck (excluding the wheels) is 276 in². The closest response is:
234 in.2
Surface area of the cab section (rectangular prism on the left):
- Front and back faces: 2 in. x 3 in. = 6 in² x 2 = 12 in²
- Top and bottom faces: 2 in. x 3 in. = 6 in² x 2 = 12 in²
- Side faces: 3 in. x 3 in. = 9 in² x 2 = 18 in²
Total surface area of the cab section = 12 in² + 12 in² + 18 in² = 42 in²
Surface area of the cargo section (rectangular prism on the right):
- Front and back faces: 6 in. x 3 in. = 18 in² x 2 = 36 in²
- Top and bottom faces: 6 in. x 11 in. = 66 in² x 2 = 132 in²
- Side faces: 3 in. x 11 in. = 33 in² x 2 = 66 in²
Total surface area of the cargo section = 36 in² + 132 in² + 66 in² = 234 in²
Adding the surface areas of the cab section and cargo section together: 42 in² + 234 in² = 276 in²
Therefore, the total surface area of the truck (excluding the wheels) is 276 in². The closest response is:
234 in.2
4 answers