Math Problem Statement

Match the surface areas and volumes with the correct formulas for different geometric shapes.

Solution

The image shows a matching problem where formulas must be matched to the correct geometric shape or surface/volume type. Below is the correct matching:

  1. Oberfläche vom Würfel ("Surface area of a cube") → C (O = 6a²)
  2. Volumen von der Pyramide ("Volume of a pyramid") → B (V = (G · h)/3)
  3. Mantel des Kegels ("Lateral surface area of a cone") → G (M = πrs)
  4. Volumen der Kugel ("Volume of a sphere") → F (V = 4/3πr³)
  5. Oberfläche des Quaders ("Surface area of a rectangular prism") → D (O = 2(ab + ac + bc))
  6. Volumen vom Würfel ("Volume of a cube") → E (V = a³)
  7. Mantel des Zylinders ("Lateral surface area of a cylinder") → A (M = 2πrh)
  8. Oberfläche der Kugel ("Surface area of a sphere") → H (O = 4πr²)

Would you like further explanations for any of the formulas?

Here are 5 related questions:

  1. What is the formula for the volume of a cone?
  2. How do you calculate the surface area of a cylinder?
  3. How does the surface area of a pyramid differ from that of a cone?
  4. Can the formula for the volume of a pyramid be used for any pyramid?
  5. What is the relationship between the volume and surface area of a sphere?

Tip: To distinguish between different shapes, remember that the lateral area refers to only the sides, while total surface area includes all faces.

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Math Problem Analysis

Mathematical Concepts

Geometry
Surface Area
Volume
Formulas for 3D shapes

Formulas

Surface area of cube: O = 6a²
Volume of pyramid: V = (G · h)/3
Lateral surface area of cone: M = πrs
Volume of sphere: V = 4/3πr³
Surface area of rectangular prism: O = 2(ab + ac + bc)
Volume of cube: V = a³
Lateral surface area of cylinder: M = 2πrh
Surface area of sphere: O = 4πr²

Theorems

Pythagorean theorem (used in deriving lateral area)
Geometric volume formulas

Suitable Grade Level

Grades 8-10