Math Problem Statement
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:
- Oberfläche vom Würfel ("Surface area of a cube") → C (O = 6a²)
- Volumen von der Pyramide ("Volume of a pyramid") → B (V = (G · h)/3)
- Mantel des Kegels ("Lateral surface area of a cone") → G (M = πrs)
- Volumen der Kugel ("Volume of a sphere") → F (V = 4/3πr³)
- Oberfläche des Quaders ("Surface area of a rectangular prism") → D (O = 2(ab + ac + bc))
- Volumen vom Würfel ("Volume of a cube") → E (V = a³)
- Mantel des Zylinders ("Lateral surface area of a cylinder") → A (M = 2πrh)
- 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:
- What is the formula for the volume of a cone?
- How do you calculate the surface area of a cylinder?
- How does the surface area of a pyramid differ from that of a cone?
- Can the formula for the volume of a pyramid be used for any pyramid?
- 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.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
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
Related Recommendation
Tips for Finding Surface Areas and Volumes of Common Shapes
Surface Area and Volume of 3D Shapes: Cube, Prism, Sphere, and Cylinder
3D Geometry: Volume and Surface Area of Cones, Pyramids, Cylinders, and Prisms
How to Find the Surface Area of Common Shapes: Sphere, Cylinder, Cone, and Prisms
Surface Area and Volume Calculations for Shapes