To find the total surface area, we need to find the surface area of each individual face and then subtract the area of the connecting sides.
For the larger rectangular prism:
- Top and bottom faces: 15 inches x 6 inches = 90 square inches each
- Front and back faces: 15 inches x 12 inches = 180 square inches each
- Left and right faces: 12 inches x 6 inches = 72 square inches each
Total surface area of the larger rectangular prism = 2(90) + 2(180) + 2(72) = 180 + 360 + 144 = 684 square inches
For the missing section:
- Top and bottom faces: 7 inches x 6 inches = 42 square inches each
- Front and back faces: 7 inches x 12 inches = 84 square inches each
- Left and right faces: 6 inches x 6 inches = 36 square inches each
Total surface area of the missing section = 2(42) + 2(84) + 2(36) = 84 + 168 + 72 = 324 square inches
Total surface area of the figure = 684 + 324 = 1008 square inches.
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 15 inches, a width of 6 inches, and a height of 12 inches. The missing section is removed from the top center of the rectangular prism. The missing section is a rectangular prism with a length of 7 inches, and a height of 6 inches. The missing section has the same width as the larger rectangular prism. The missing section is centered at the top of the larger rectangular prism. The remaining lengths to the left and right of the missing section both measure 4 inches.
What is the total surface area of the figure?
please subtract the connecting sides
11 answers
wrong
I apologize for the mistake. Let's correct the calculation.
For the larger rectangular prism:
- Top and bottom faces: 15 inches x 6 inches = 90 square inches each
- Front and back faces: 15 inches x 12 inches = 180 square inches each
- Left and right faces: 12 inches x 6 inches = 72 square inches each
Total surface area of the larger rectangular prism = 2(90) + 2(180) + 2(72) = 180 + 360 + 144 = 684 square inches
For the missing section:
- Top and bottom faces: 7 inches x 6 inches = 42 square inches each
- Front and back faces: 7 inches x 6 inches = 42 square inches each
- Left and right faces: 6 inches x 6 inches = 36 square inches each
Total surface area of the missing section = 2(42) + 2(42) + 2(36) = 84 + 84 + 72 = 240 square inches
Now, to find the total surface area of the figure, we subtract the area of the connecting sides, which are the top faces of the larger rectangular prism and the missing section (since they would be connected):
- Area of the connecting sides = 15 inches x 6 inches = 90 square inches
Total surface area of the figure = Sum of surface area of the larger rectangular prism + Sum of surface area of the missing section - Area of the connecting sides
Total surface area = 684 + 240 - 90 = 834 square inches
Therefore, the total surface area of the figure is 834 square inches. Thank you for your patience.
For the larger rectangular prism:
- Top and bottom faces: 15 inches x 6 inches = 90 square inches each
- Front and back faces: 15 inches x 12 inches = 180 square inches each
- Left and right faces: 12 inches x 6 inches = 72 square inches each
Total surface area of the larger rectangular prism = 2(90) + 2(180) + 2(72) = 180 + 360 + 144 = 684 square inches
For the missing section:
- Top and bottom faces: 7 inches x 6 inches = 42 square inches each
- Front and back faces: 7 inches x 6 inches = 42 square inches each
- Left and right faces: 6 inches x 6 inches = 36 square inches each
Total surface area of the missing section = 2(42) + 2(42) + 2(36) = 84 + 84 + 72 = 240 square inches
Now, to find the total surface area of the figure, we subtract the area of the connecting sides, which are the top faces of the larger rectangular prism and the missing section (since they would be connected):
- Area of the connecting sides = 15 inches x 6 inches = 90 square inches
Total surface area of the figure = Sum of surface area of the larger rectangular prism + Sum of surface area of the missing section - Area of the connecting sides
Total surface area = 684 + 240 - 90 = 834 square inches
Therefore, the total surface area of the figure is 834 square inches. Thank you for your patience.
still wrong
I apologize for the error. Let's recalculate the total surface area of the figure.
For the larger rectangular prism:
- Top and bottom faces: 15 inches x 6 inches = 90 square inches each
- Front and back faces: 15 inches x 12 inches = 180 square inches each
- Left and right faces: 12 inches x 6 inches = 72 square inches each
Total surface area of the larger rectangular prism = 2(90) + 2(180) + 2(72) = 180 + 360 + 144 = 684 square inches
For the missing section:
- Top and bottom faces: 7 inches x 6 inches = 42 square inches each
- Front and back faces: 7 inches x 12 inches = 84 square inches each
- Left and right faces: 6 inches x 6 inches = 36 square inches each
Total surface area of the missing section = 2(42) + 2(84) + 2(36) = 84 + 168 + 72 = 324 square inches
Total surface area of the figure = Sum of surface area of the larger rectangular prism + Sum of surface area of the missing section - 2 times the area of the connecting sides (top faces of the larger rectangular prism and missing section)
Total surface area = 684 + 324 - 2(90) = 684 + 324 - 180 = 828 square inches
Therefore, the correct total surface area of the figure is 828 square inches. Thank you for your patience.
For the larger rectangular prism:
- Top and bottom faces: 15 inches x 6 inches = 90 square inches each
- Front and back faces: 15 inches x 12 inches = 180 square inches each
- Left and right faces: 12 inches x 6 inches = 72 square inches each
Total surface area of the larger rectangular prism = 2(90) + 2(180) + 2(72) = 180 + 360 + 144 = 684 square inches
For the missing section:
- Top and bottom faces: 7 inches x 6 inches = 42 square inches each
- Front and back faces: 7 inches x 12 inches = 84 square inches each
- Left and right faces: 6 inches x 6 inches = 36 square inches each
Total surface area of the missing section = 2(42) + 2(84) + 2(36) = 84 + 168 + 72 = 324 square inches
Total surface area of the figure = Sum of surface area of the larger rectangular prism + Sum of surface area of the missing section - 2 times the area of the connecting sides (top faces of the larger rectangular prism and missing section)
Total surface area = 684 + 324 - 2(90) = 684 + 324 - 180 = 828 square inches
Therefore, the correct total surface area of the figure is 828 square inches. Thank you for your patience.
split the figure into 2 cubes and 1 rectangular prism
Let's split the figure into 2 cubes and 1 rectangular prism to find the total surface area.
1. Larger Cube:
- Dimensions: 6 inches x 6 inches x 6 inches
- Surface area: 6 faces x (6 inches x 6 inches) = 6 x 36 = 216 square inches
2. Smaller Cube:
- Dimensions: 7 inches x 7 inches x 7 inches
- Surface area: 6 faces x (7 inches x 7 inches) = 6 x 49 = 294 square inches
3. Long Rectangular Prism:
- Dimensions: 6 inches x 6 inches x 15 inches
- Surface area: 2(6 inches x 6 inches) + 2(6 inches x 15 inches) + 2(6 inches x 15 inches) = 72 + 180 + 180 = 432 square inches
Total surface area = Surface area of larger cube + Surface area of smaller cube + Surface area of long rectangular prism
Total surface area = 216 + 294 + 432 = 942 square inches
Therefore, the total surface area of the figure when split into two cubes and one rectangular prism is 942 square inches. Thank you for guiding me to the correct solution.
1. Larger Cube:
- Dimensions: 6 inches x 6 inches x 6 inches
- Surface area: 6 faces x (6 inches x 6 inches) = 6 x 36 = 216 square inches
2. Smaller Cube:
- Dimensions: 7 inches x 7 inches x 7 inches
- Surface area: 6 faces x (7 inches x 7 inches) = 6 x 49 = 294 square inches
3. Long Rectangular Prism:
- Dimensions: 6 inches x 6 inches x 15 inches
- Surface area: 2(6 inches x 6 inches) + 2(6 inches x 15 inches) + 2(6 inches x 15 inches) = 72 + 180 + 180 = 432 square inches
Total surface area = Surface area of larger cube + Surface area of smaller cube + Surface area of long rectangular prism
Total surface area = 216 + 294 + 432 = 942 square inches
Therefore, the total surface area of the figure when split into two cubes and one rectangular prism is 942 square inches. Thank you for guiding me to the correct solution.
still incorrect
I apologize for the oversight in the previous calculations. Let's reanalyze the figure by splitting it into two cubes and one rectangular prism to find the correct total surface area.
Splitting the figure into components:
1. Larger Cube:
- Dimensions: 6 inches x 6 inches x 6 inches
- Surface Area: 6 faces x (6 inches x 6 inches) = 6 x 36 = 216 square inches
2. Smaller Cube (missing section):
- Dimensions: 6 inches x 6 inches x 6 inches
- Surface Area: 6 faces x (6 inches x 6 inches) = 6 x 36 = 216 square inches
3. Rectangular Prism:
- Dimensions: 15 inches x 6 inches x 6 inches (with top center missing)
- Surface Area: 2(15 inches x 6 inches) + 2(6 inches x 6 inches) = 180 + 72 = 252 square inches
- Subtract the top surface area that is missing: 15 inches x 6 inches = 90 square inches
Total Surface Area = Surface Area of Larger Cube + Surface Area of Smaller Cube + Surface Area of Rectangular Prism - Area of Missing Top Surface
Total Surface Area = 216 + 216 + 252 - 90 = 594 square inches
Therefore, the correct total surface area of the figure when split into two cubes and one rectangular prism is 594 square inches. Thank you for your patience, and I appreciate your guidance.
Splitting the figure into components:
1. Larger Cube:
- Dimensions: 6 inches x 6 inches x 6 inches
- Surface Area: 6 faces x (6 inches x 6 inches) = 6 x 36 = 216 square inches
2. Smaller Cube (missing section):
- Dimensions: 6 inches x 6 inches x 6 inches
- Surface Area: 6 faces x (6 inches x 6 inches) = 6 x 36 = 216 square inches
3. Rectangular Prism:
- Dimensions: 15 inches x 6 inches x 6 inches (with top center missing)
- Surface Area: 2(15 inches x 6 inches) + 2(6 inches x 6 inches) = 180 + 72 = 252 square inches
- Subtract the top surface area that is missing: 15 inches x 6 inches = 90 square inches
Total Surface Area = Surface Area of Larger Cube + Surface Area of Smaller Cube + Surface Area of Rectangular Prism - Area of Missing Top Surface
Total Surface Area = 216 + 216 + 252 - 90 = 594 square inches
Therefore, the correct total surface area of the figure when split into two cubes and one rectangular prism is 594 square inches. Thank you for your patience, and I appreciate your guidance.
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 15 inches, a width of 6 inches, and a height of 12 inches. The missing section is removed from the top center of the rectangular prism. The missing section is a rectangular prism with a length of 7 inches, and a height of 6 inches. The missing section has the same width as the larger rectangular prism. The missing section is centered at the top of the larger rectangular prism. The remaining lengths to the left and right of the missing section both measure 4 inches.
What is the total surface area of the figure?
(1 point)
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 15 inches, a width of 6 inches, and a height of 12 inches. The missing section is removed from the top center of the rectangular prism. The missing section is a rectangular prism with a length of 7 inches, and a height of 6 inches. The missing section has the same width as the larger rectangular prism. The missing section is centered at the top of the larger rectangular prism. The remaining lengths to the left and right of the missing section both measure 4 inches.
What is the total surface area of the figure?
(1 point)
To calculate the total surface area of the figure, we need to consider the individual surface areas of the visible faces while taking into account the missing section.
- Surface area of the larger rectangular prism:
- Top and bottom faces: 15 inches x 6 inches = 90 square inches each
- Front and back faces: 15 inches x 12 inches = 180 square inches each
- Left and right faces: 12 inches x 6 inches = 72 square inches each
- Total surface area of the larger rectangular prism = 2(90) + 2(180) + 2(72) = 180 + 360 + 144 = 684 square inches
- Surface area of the missing section:
- Top and bottom faces: 7 inches x 6 inches = 42 square inches each
- Front and back faces: 7 inches x 6 inches = 42 square inches each
- Left and right faces: 6 inches x 6 inches = 36 square inches each
- Total surface area of the missing section = 2(42) + 2(42) + 2(36) = 84 + 84 + 72 = 240 square inches
To find the total surface area of the figure, we subtract the overlapping area (top surface of the missing section):
- Overlapping area = 7 inches x 6 inches = 42 square inches
Therefore, the total surface area of the figure is:
684 square inches (surface area of the larger rectangular prism) - 240 square inches (surface area of the missing section) + 42 square inches (overlapping area) = 486 square inches.
So, the total surface area of the figure is 486 square inches.
- Surface area of the larger rectangular prism:
- Top and bottom faces: 15 inches x 6 inches = 90 square inches each
- Front and back faces: 15 inches x 12 inches = 180 square inches each
- Left and right faces: 12 inches x 6 inches = 72 square inches each
- Total surface area of the larger rectangular prism = 2(90) + 2(180) + 2(72) = 180 + 360 + 144 = 684 square inches
- Surface area of the missing section:
- Top and bottom faces: 7 inches x 6 inches = 42 square inches each
- Front and back faces: 7 inches x 6 inches = 42 square inches each
- Left and right faces: 6 inches x 6 inches = 36 square inches each
- Total surface area of the missing section = 2(42) + 2(42) + 2(36) = 84 + 84 + 72 = 240 square inches
To find the total surface area of the figure, we subtract the overlapping area (top surface of the missing section):
- Overlapping area = 7 inches x 6 inches = 42 square inches
Therefore, the total surface area of the figure is:
684 square inches (surface area of the larger rectangular prism) - 240 square inches (surface area of the missing section) + 42 square inches (overlapping area) = 486 square inches.
So, the total surface area of the figure is 486 square inches.
1 answer