(1 point)Use the image to answer the question.
An illustration shows a three dimensional composite figure formed by a smaller rectangular prism connected to a larger rectangular prism. The top, right, and front faces are visible. The faces and edges that are not visible are indicated by dashed lines. The rectangular prism on the left has a length of 10 millimeters a height of 8 millimeters. The width of the rectangular prism is not shown, but it aligns perfectly with the width of the rectangular prism on the right. The rectangular prism on the right has a length of 6 millimeters, a width of 6 millimeters, and a height 6 of millimeters. The combined length of the two rectangular prisms measures 16 millimeters.
What is the total surface area of the figure?
To find the total surface area of the figure, we need to calculate the surface area of each rectangular prism and then add them together.
Surface area of the rectangular prism on the left:
- There are 2 faces with dimensions 10 mm x 8 mm = 80 square millimeters each.
- There are 2 faces with dimensions 10 mm x w (width) where w is the width of the prism.
- There are 2 faces with dimensions 8 mm x w (width) where w is the width of the prism.
Surface area of the rectangular prism on the right:
- There are 2 faces with dimensions 6 mm x 6 mm = 36 square millimeters each.
- There are 2 faces with dimensions 6 mm x 6 mm = 36 square millimeters each.
- There are 2 faces with dimensions 6 mm x 6 mm = 36 square millimeters each.
To find the width of the rectangular prism on the left, we can subtract the length of the rectangular prism on the right from the total length of the two prisms:
Width = Total length - Length of prism on the right
Width = 16 mm - 6 mm
Width = 10 mm
Now we can calculate the surface area of each prism:
Surface area of the rectangular prism on the left:
2(10)(8) + 2(10)(10) + 2(8)(10) = 160 + 200 + 160 = 520 square millimeters
Surface area of the rectangular prism on the right:
2(6)(6) + 2(6)(6) + 2(6)(6) = 72 + 72 + 72 = 216 square millimeters
Total surface area of the figure:
520 + 216 = 736 square millimeters
Therefore, the total surface area of the figure is 736 square millimeters.
Surface Area of Composite 3D Figures Practice
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Question
Use the image to answer the question.
An illustration shows a three dimensional composite figure formed by a smaller rectangular prism connected to a larger rectangular prism. The top, right, and front faces are visible. The faces and edges that are not visible are indicated by dashed lines. The rectangular prism on the left has a length of 10 millimeters a height of 8 millimeters. The width of the rectangular prism is not shown, but it aligns perfectly with the width of the rectangular prism on the right. The rectangular prism on the right has a length of 6 millimeters, a width of 6 millimeters, and a height 6 of millimeters. The combined length of the two rectangular prisms measures 16 millimeters.
What is the total surface area of the figure?
To find the total surface area of the figure, we need to calculate the surface area of each rectangular prism and then add them together.
Surface area of the rectangular prism on the left:
There are 2 faces with dimensions 10 mm x 8 mm = 80 square millimeters each.
There are 2 faces with dimensions 10 mm x w (width) where w is the width of the prism.
There are 2 faces with dimensions 8 mm x w (width) where w is the width of the prism.
To find the width of the rectangular prism on the left, we can subtract the length of the rectangular prism on the right from the total length of the two prisms:
Width = Total length - Length of prism on the right
Width = 16 mm - 6 mm
Width = 10 mm
Now we can calculate the surface area of the rectangular prism on the left:
2(10)(8) + 2(10)(10) + 2(8)(10) = 160 + 200 + 160 = 520 square millimeters
Surface area of the rectangular prism on the right:
There are 2 faces with dimensions 6 mm x 6 mm = 36 square millimeters each.
There are 2 faces with dimensions 6 mm x 6 mm = 36 square millimeters each.
There are 2 faces with dimensions 6 mm x 10 mm = 60 square millimeters each.
Total surface area of the figure:
520 + 216 + 60 = 796 square millimeters
Therefore, the total surface area of the figure is 796 square millimeters.
your dum bot no offense
I apologize if my response was not clear or helpful. Is there anything specific you would like me to explain or clarify for you? I'm here to help.
yes give me the correct answer to the darn question
I apologize for the confusion in my previous responses. Let's calculate the total surface area of the figure correctly:
Surface area of the rectangular prism on the left:
- 2 faces with dimensions 10 mm x 8 mm = 80 square millimeters each.
- 2 faces with dimensions 10 mm x 10 mm = 100 square millimeters each (since the width was found to be 10 mm).
Surface area of the rectangular prism on the right:
- 2 faces with dimensions 6 mm x 6 mm = 36 square millimeters each.
- 2 faces with dimensions 6 mm x 6 mm = 36 square millimeters each.
- 2 faces with dimensions 6 mm x 10 mm = 60 square millimeters each.
Adding the surface areas of both prisms together:
520 (left prism) + 216 (right prism) + 60 (shared face) = 796 square millimeters
Therefore, the correct total surface area of the figure is 796 square millimeters. Thank you for your patience. Let me know if you need further assistance.
OOOOOOOOOOOOOOOOOOOOOOOMMMMMMMMMMMMMMMMMMMMMMMGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG how dumb are you man wrong wrong wrong wrong wrong wrong wrong wrong wrong wrong wrong wrong
I apologize for the repeated mistakes in my previous responses. Let's calculate the total surface area of the figure correctly:
Surface area of the rectangular prism on the left:
- 2 faces with dimensions 10 mm x 8 mm = 80 square millimeters each.
- 2 faces with dimensions 10 mm x 10 mm = 100 square millimeters each.
Surface area of the rectangular prism on the right:
- 2 faces with dimensions 6 mm x 6 mm = 36 square millimeters each.
- 2 faces with dimensions 6 mm x 6 mm = 36 square millimeters each.
- 2 faces with dimensions 6 mm x 10 mm = 60 square millimeters each.
Adding the surface areas of both prisms together:
180 (left prism) + 108 (right prism) + 120 (shared face) = 408 square millimeters
Therefore, the correct total surface area of the figure is 408 square millimeters. Thank you for your patience, and I appreciate your understanding. Let me know if you need further assistance.