Math Problem Statement
answer these questions
Solution
It seems like you've uploaded images with two distinct questions. Let's address each one:
First Image: Surface Area of the Figure
The first image involves calculating the surface area of a figure, which looks like a combination of a rectangular prism and an extended shape.
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Dimensions of the figure:
- Length: 20 m
- Width: 12 m
- Height: 4 m (for the part that extends out)
We can break the surface area calculation into parts:
- The surface area of the long rectangular section.
- The surface area of the smaller rectangular block attached to the long section.
To calculate the surface area of the entire figure:
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For the first rectangular prism (the long part):
- Top and bottom faces:
- Front and back faces:
- Left and right faces:
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For the attached smaller rectangular prism:
- Top and bottom faces:
- Front and back faces:
- Left and right faces:
Summing up these areas will give the total surface area.
Second Image: Volume of the Figure
This figure seems like an L-shaped block. To calculate the volume of such a figure, we need to consider the shape as a combination of two rectangular prisms:
- The larger section (18 mm by 7 mm by 4 mm).
- The smaller section (2 mm by 4 mm by 4 mm) that is subtracted from it.
Volume Calculation:
- Volume of the large rectangular prism = mm³
- Volume of the smaller rectangular prism = mm³
The total volume will be the difference between these two volumes:
Would you like further assistance with the calculations or need more details? Feel free to ask!
Here are 5 related questions:
- How do you calculate the surface area of complex 3D shapes?
- How can you break down the volume of composite shapes like L-shaped figures?
- What is the difference between surface area and volume calculations for 3D objects?
- How does the positioning of a smaller block affect the surface area of the overall figure?
- Why is it important to subtract the volume of the cut-out section in complex shapes?
Tip: Always carefully break down complex figures into simpler shapes to make calculations easier.
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Math Problem Analysis
Mathematical Concepts
Surface Area
Volume
Rectangular Prism
L-shaped Figures
Formulas
Surface Area of Rectangular Prism: 2 * (Length * Width + Length * Height + Width * Height)
Volume of Rectangular Prism: Length * Width * Height
Volume of Composite Shapes: Volume of Larger Section - Volume of Smaller Section
Theorems
Volume and Surface Area of Prisms
Composite Shape Calculations
Suitable Grade Level
Grades 7-9