Math Problem Statement
Solution
To calculate the volume of the shape, which is made up of a cuboid and a pyramid, we break the calculation into two parts:
Step 1: Volume of the Cuboid
The dimensions of the cuboid are:
- Length = 20 cm
- Width = 20 cm
- Height = 32 cm
The volume of a cuboid is given by:
Step 2: Volume of the Pyramid
The base of the pyramid is a square with side 20 cm, and its height is 15 cm.
The volume of a pyramid is given by:
Step 3: Total Volume of the Shape
Final Answer:
The volume of the shape is:
Let me know if you'd like further clarification or additional details.
Questions for exploration:
- How would the volume change if the height of the pyramid increased?
- What is the surface area of the combined shape?
- How do you calculate the volume for shapes with irregular bases?
- What is the ratio of the volume of the pyramid to the volume of the cuboid?
- How would the calculations differ if the pyramid were a cone?
Tip:
When solving problems involving combined 3D shapes, always separate the calculations for each component and ensure consistency in units!
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Math Problem Analysis
Mathematical Concepts
Volume calculation
3D geometry
Addition of volumes
Formulas
Volume of a cuboid = length × width × height
Volume of a pyramid = (1/3) × base area × height
Theorems
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Suitable Grade Level
Grades 6-8
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