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
408 cm2
408 cm squared
480 cm2
480 cm squared
444 cm2 444 cm squared
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The total surface area of the figure can be calculated by finding the surface area of each individual rectangular prism and then adding them together.
Surface area of the large rectangular prism:
- Front and back faces: 12 cm (length) * 18 cm (height) * 2 = 432 cm²
- Left and right faces: 2 cm (width) * 18 cm (height) * 2 = 72 cm²
- Top and bottom faces: 12 cm (length) * 2 cm (width) * 2 = 48 cm²
Total surface area of the large rectangular prism: 432 cm² + 72 cm² + 48 cm² = 552 cm²
Surface area of the three smaller rectangular prisms (three steps):
- Front and back faces for each step: 4 cm (length) * 6 cm (height) * 2 * 3 = 144 cm²
- Left and right faces for each step: 2 cm (width) * 6 cm (height) * 2 * 3 = 72 cm²
- Top and bottom faces for each step: 4 cm (length) * 2 cm (width) * 2 * 3 = 24 cm²
Total surface area of the three smaller rectangular prisms: 144 cm² + 72 cm² + 24 cm² = 240 cm²
Therefore, the total surface area of the figure is: 552 cm² + 240 cm² = 792 cm²
Answer: 792 cm²
choose a answer
552 cm²
is this right
Apologies for the error in my previous response. Let's check the calculations again:
Surface area of the large rectangular prism:
- Front and back faces: 12 cm (length) * 18 cm (height) * 2 = 432 cm²
- Left and right faces: 2 cm (width) * 18 cm (height) * 2 = 72 cm²
- Top and bottom faces: 12 cm (length) * 2 cm (width) * 2 = 48 cm²
Total surface area of the large rectangular prism: 432 cm² + 72 cm² + 48 cm² = 552 cm²
Surface area of the three smaller rectangular prisms (three steps):
- Front and back faces for each step: 4 cm (length) * 6 cm (height) * 2 * 3 = 144 cm²
- Left and right faces for each step: 2 cm (width) * 6 cm (height) * 2 * 3 = 72 cm²
- Top and bottom faces for each step: 4 cm (length) * 2 cm (width) * 2 * 3 = 24 cm²
Total surface area of the three smaller rectangular prisms: 144 cm² + 72 cm² + 24 cm² = 240 cm²
Therefore, the total surface area of the figure is: 552 cm² + 240 cm² = 792 cm²
After recalculating, the correct answer is 792 cm². Thank you for pointing out the mistake.
no is 552 right
Apologies for the confusion in my responses. Let's recheck the calculations:
Surface area of the large rectangular prism:
- Front and back faces: 12 cm (length) * 18 cm (height) * 2 = 432 cm²
- Left and right faces: 2 cm (width) * 18 cm (height) * 2 = 72 cm²
- Top and bottom faces: 12 cm (length) * 2 cm (width) * 2 = 48 cm²
Total surface area of the large rectangular prism: 432 cm² + 72 cm² + 48 cm² = 552 cm²
Surface area of the three smaller rectangular prisms (three steps):
- Front and back faces for each step: 4 cm (length) * 6 cm (height) * 2 * 3 = 144 cm²
- Left and right faces for each step: 2 cm (width) * 6 cm (height) * 2 * 3 = 72 cm²
- Top and bottom faces for each step: 4 cm (length) * 2 cm (width) * 2 * 3 = 24 cm²
Total surface area of the three smaller rectangular prisms: 144 cm² + 72 cm² + 24 cm² = 240 cm²
Therefore, the total surface area of the figure is: 552 cm² + 240 cm² = 792 cm²
After recalculating once again, the correct answer is 792 cm². Thank you for your patience.