Math Problem Statement

answer these questions

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.

  1. 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:

  • For the first rectangular prism (the long part):

    • Top and bottom faces: 2×(20×12)2 \times (20 \times 12)
    • Front and back faces: 2×(20×4)2 \times (20 \times 4)
    • Left and right faces: 2×(12×4)2 \times (12 \times 4)
  • For the attached smaller rectangular prism:

    • Top and bottom faces: 2×(4×12)2 \times (4 \times 12)
    • Front and back faces: 2×(4×4)2 \times (4 \times 4)
    • Left and right faces: 2×(12×4)2 \times (12 \times 4)

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 = 18×7×418 \times 7 \times 4 mm³
  • Volume of the smaller rectangular prism = 2×4×42 \times 4 \times 4 mm³

The total volume will be the difference between these two volumes: Volume=Volume of larger sectionVolume of smaller section\text{Volume} = \text{Volume of larger section} - \text{Volume of smaller section}


Would you like further assistance with the calculations or need more details? Feel free to ask!

Here are 5 related questions:

  1. How do you calculate the surface area of complex 3D shapes?
  2. How can you break down the volume of composite shapes like L-shaped figures?
  3. What is the difference between surface area and volume calculations for 3D objects?
  4. How does the positioning of a smaller block affect the surface area of the overall figure?
  5. 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