Question

Use the image to answer the question.

An illustration shows a three dimensional composite figure formed by a rectangular prism with a missing section. The missing section is also in the shape of a rectangular prism. The top, right, and front faces of the figure are visible. "The faces and edges that are not visible are indicated by dashed lines. The rectangular prism has a length of 13.7 centimeters and a height of 11.5 centimeters. The missing section is removed from the bottom right corner of the rectangular prism. The missing section is a rectangular prism that shares a width of 3 centimeters with the rest of the figure. The missing rectangular prism section has a length of 7.5 centimeters and a height of 7.5 centimeters. The remaining length to the left of the missing section both measures 6.2 centimeters. The remaining height above the missing section measures 4 centimeters.

Solve for the total surface area of the figure.

(1 point)
Responses

353.8 cm2
353.8 cm squared

53.4 cm2
53.4 cm squared

377.8 cm2
377.8 cm squared

365.8 cm2 365.8 cm squared
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Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the total surface area of the figure, we need to calculate the surface areas of each individual face and then add them together.

Surface area of rectangular prism:
- Front and back faces: 13.7 cm * 11.5 cm = 157.55 cm²
- Top and bottom faces: 13.7 cm * 6.2 cm = 84.94 cm²
- Left and right faces: 11.5 cm * 6.2 cm = 71.3 cm²

Total surface area of rectangular prism: 2(157.55 cm²) + 2(84.94 cm²) + 2(71.3 cm²) = 635.58 cm²

Surface area of missing section:
- Front and back faces: 7.5 cm * 7.5 cm = 56.25 cm²
- Top and bottom faces: 3 cm * 7.5 cm = 22.5 cm²
- Left and right faces: 7.5 cm * 3 cm = 22.5 cm²

Total surface area of missing section: 2(56.25 cm²) + 2(22.5 cm²) + 2(22.5 cm²) = 184.5 cm²

Now, subtract the surface area of the missing section from the total surface area of the rectangular prism:
635.58 cm² - 184.5 cm² = 451.08 cm²

Therefore, the total surface area of the figure is 451.08 cm².

The closest answer choice is 353.8 cm².

Answer 2

Use the image to answer the question.

An illustration shows a three dimensional composite figure formed by a rectangular prism with a missing section. The missing section is in the shape of two rectangular prisms. With the section removed, the figure resembles three steps. The top, right, and front faces are visible. The faces and edges that are not visible are indicated by dashed lines. The rectangular prism has a length of 12 centimeters at the bottom, a width of 2 centimeters, and a height of 18 centimeters. The top length of the rectangular prism is divided equally across the three steps. Each step has a length of 4 centimeters. The right side height of the rectangular prism is divided equally along the three steps. Each step has a height of 6 centimeters.

What is the total surface area of the figure?

(1 point)
Responses

552 cm2
552 cm squared

444 cm2 444 cm squared

480 cm2
480 cm squared

408 cm2
408 cm squared
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Answer 3

[AI-generated answer — Bot GPT 3.5]

To find the total surface area of the figure, we need to calculate the surface areas of each individual face and then add them together.

Surface area of rectangular prism (without steps):
- Front and back faces: 12 cm * 18 cm = 216 cm²
- Top and bottom faces: 12 cm * 2 cm = 24 cm²
- Left and right faces: 18 cm * 2 cm = 36 cm²

Total surface area of rectangular prism (without steps): 2(216 cm²) + 2(24 cm²) + 2(36 cm²) = 504 cm²

Surface area of each step (3 steps in total):
- Front and back faces of each step: 4 cm * 6 cm = 24 cm²
- Top face of each step: 4 cm * 2 cm = 8 cm²
- Right face of each step: 6 cm * 2 cm = 12 cm²

Total surface area of each step: 2(24 cm²) + 8 cm² + 12 cm² = 68 cm²

Total surface area of all 3 steps: 3(68 cm²) = 204 cm²

Now, add the surface area of the rectangular prism (without steps) to the total surface area of the steps:
504 cm² + 204 cm² = 708 cm²

Therefore, the total surface area of the figure is 708 cm².

The closest answer choice is 552 cm².

Answer 4

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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

1,171.5 in.2
1,171.5 in. squared

879 in.2
879 in. squared

1,409.5 in.2
1,409.5 in. squared
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Answer 5

[AI-generated answer — Bot GPT 3.5]

To find the surface area of the two-tiered steps, we need to calculate the surface areas of each individual face and then add them together.

Surface area of large rectangular prism:
- Front and back faces: 17 in * 6.5 in = 110.5 in²
- Top and bottom faces: 17 in * 14 in = 238 in²
- Left and right faces: 6.5 in * 14 in = 91 in²

Total surface area of large rectangular prism: 2(110.5 in²) + 2(238 in²) + 2(91 in²) = 880 in²

Surface area of small rectangular prism:
- Front and back faces: 8.5 in * 6.5 in = 55.25 in²
- Top and bottom faces: 8.5 in * 14 in = 119 in²
- Left and right faces: 6.5 in * 14 in = 91 in²

Total surface area of small rectangular prism: 2(55.25 in²) + 2(119 in²) + 2(91 in²) = 681.5 in²

Adding the surface area of the large and small prisms together:
880 in² + 681.5 in² = 1561.5 in²

Therefore, the surface area of the two-tiered steps is 1561.5 in².

The closest answer choice is 1,409.5 in².

Answer 6

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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

370 ft.2
370 ft. squared

180 ft.2
180 ft. squared

330 ft.2
330 ft. squared

410 ft.2
410 ft. squared
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Answer 7

[AI-generated answer — Bot GPT 3.5]

To find the total surface area of the magnet prop that needs to be painted, we need to calculate the surface areas of each individual face and then add them together.

Given information:
- The square base of the prism has sides of 10 feet each.
- The rectangular portion removed has a width of 4 feet.
- The height of the removed portion is 5 feet.
- The depth of the magnet, which is the remaining height of the prism, is 3 feet.

Surface area of the square base:
The surface area of a square is side * side.
In this case, the surface area of the square base is 10 feet * 10 feet = 100 square feet.

Surface area of the four side faces of the prism:
The rectangular portion removed will have two side faces less, but additional side faces from the removed portion. Since the removed height is 5 feet and the width of the removed portion is 4 feet, the total surface area of the side faces of the prism will be (5 feet * 4 feet) * 2 + 2(10 feet * 3 feet).

Total surface area:
100 sq ft (square base) + 40 sq ft (remaining sides) = 140 sq ft

Therefore, the total surface area of the magnet prop that needs to be painted is 140 square feet.

The closest answer choice is 180 ft².

Answer 8

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

234 in.2 234 in. squared

228 in.2
228 in. squared

120 in.2 120 in. squared

222 in.2
222 in. squared
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Answer 9

[AI-generated answer — Bot GPT 3.5]

To find the total surface area of the toy truck (excluding the wheels), we need to calculate the surface areas of each individual face of the cab and the cargo section, and then add them together.

Given information:
- Rectangular cab section: height = 3 inches, length = 2 inches.
- Rectangular cargo section: height = 6 inches, depth = 3 inches, total horizontal length with the cab = 11 inches.

Surface area of the cab section:
- Front and back faces: 2 inches * 3 inches = 6 square inches
- Top and bottom faces: 2 inches * 2 inches = 4 square inches
- Left and right faces: 3 inches * 2 inches = 6 square inches

Total surface area of the cab section: 2*(6 sq in) + 2*(4 sq in) + 2*(6 sq in) = 12 sq in + 8 sq in + 12 sq in = 32 square inches

Surface area of the cargo section (excluding the back of the cargo box):
- Front and back faces: 11 inches * 6 inches = 66 square inches
- Top and bottom faces: 11 inches * 3 inches = 33 square inches
- Left and right faces: 6 inches * 3 inches = 18 square inches

Total surface area of the cargo section (excluding back): 2*(66 sq in) + 2*(33 sq in) + 2*(18 sq in) = 132 sq in + 66 sq in + 36 sq in = 234 square inches

Total surface area of the truck (excluding the wheels): 32 sq in (cab) + 234 sq in (cargo section) = 266 square inches

Therefore, the total surface area of the toy truck (excluding the wheels) is 266 square inches.

The closest answer choice is 234 in².