Math Problem Statement
Solution
Let's calculate the volumes of the two compound shapes (a and b) given in the image.
Shape a
Shape is made up of two rectangular prisms:
-
Bottom section:
- Length:
- Width:
- Height:
Volume of bottom section:
-
Top section:
- Length:
- Width:
- Height:
Volume of top section:
The total volume of shape is:
Shape b
Shape is also made up of two rectangular prisms:
-
Top section:
- Length:
- Width:
- Depth:
Volume of top section:
-
Bottom section:
- Length:
- Width:
- Depth:
Volume of bottom section:
The total volume of shape is:
Final Results
- Volume of shape :
- Volume of shape :
Would you like more details or have any questions?
Related Questions:
- How would the volumes change if shape had a different height for the top section?
- What is the volume of shape in cubic centimeters?
- How can we calculate the surface area of these compound shapes?
- If shape was scaled down by half, what would be its new volume?
- What are the differences in calculating volume for other 3D shapes like cylinders or spheres?
Tip:
Always double-check that all measurements are in the same units when calculating volumes to avoid errors.
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Math Problem Analysis
Mathematical Concepts
Geometry
Volume Calculation
Rectangular Prisms
Formulas
Volume of rectangular prism = length × width × height
Theorems
-
Suitable Grade Level
Grades 7-9
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