Math Problem Statement

Die Maße sind in cm angegeben. Zeichne zu jedem Körper ein Netz. Berechne zu jedem Körper den Oberflächeninhalt. Berechne zu jedem Körper das Volumen.

Solution

The image you uploaded contains a geometry problem involving different 3D shapes. The shapes include a rectangular prism (cuboid), a trapezoidal prism, a cylinder, and another trapezoidal prism. The questions are:

a) Draw a net for each body. b) Calculate the surface area of each body. c) Calculate the volume of each body.

Let me break down each part of the task for you:

  1. Drawing the net:

    • A net is a 2D shape that can be folded to form the 3D object. I can describe how to create nets for each object.
  2. Surface Area Calculation:

    • Cuboid (Shape 1): You’ll calculate the area of the six faces (2 pairs of opposite rectangles).
    • Trapezoidal Prism (Shape 2): You'll need to calculate the areas of the trapezoidal base and the sides.
    • Cylinder (Shape 3): Surface area is the sum of the areas of the two circular bases and the side (lateral surface).
    • Trapezoidal Prism (Shape 4): Similar to the second shape, calculate the areas of the trapezoidal bases and sides.
  3. Volume Calculation:

    • Cuboid: Volume is the product of its length, width, and height.
    • Trapezoidal Prism: Volume is calculated as the area of the trapezoidal base multiplied by the height.
    • Cylinder: Volume is π times the radius squared times the height.
    • Trapezoidal Prism (Shape 4): Volume is calculated similarly to the second trapezoidal prism.

I can help with each step! Would you like to start with the surface area or volume calculations for any specific shape? Or would you like a general explanation for the whole problem?

Here are five related questions:

  1. How do you calculate the surface area of a cuboid?
  2. What are the steps for calculating the volume of a cylinder?
  3. How do you determine the area of a trapezoid?
  4. How do you draw a net for a 3D object like a cuboid?
  5. What is the formula for the volume of a trapezoidal prism?

Tip: Always double-check your unit conversions if you're working with different measurement units for length, width, and height!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Geometry
Surface Area Calculation
Volume Calculation
3D Shapes

Formulas

Surface area of a cuboid: 2(lw + lh + wh)
Volume of a cuboid: l × w × h
Surface area of a cylinder: 2πr² + 2πrh
Volume of a cylinder: πr²h
Surface area of a trapezoidal prism: Sum of all face areas
Volume of a trapezoidal prism: Base area × height

Theorems

Properties of 3D shapes
Surface area and volume theorems

Suitable Grade Level

Grades 7-10