Math Problem Statement
Solution
The image contains several rectangular prisms with their volumes and some missing dimensions. Let's go through them step-by-step and find the missing dimensions.
Problem 3
- Volume = 231 in³
- Dimensions: Length = 3 in, Width = 7 in, Height = ?
To find the missing dimension (height), we use the formula for the volume of a rectangular prism:
Substitute the known values:
Solve for :
So, the missing dimension is 11 in.
Problem 4
- Volume = 6400 m³
- Dimensions: Length = 20 m, Width = 20 m, Height = ?
Using the same volume formula:
Substitute the known values:
Solve for :
So, the missing dimension is 16 m.
Problem 5
- Volume = 18,000 cm³
- Dimensions: Length = ?, Width = 8 cm, Height = 30 cm
Using the formula:
Substitute the known values:
Solve for :
So, the missing dimension is 75 cm.
Problem 6
- Volume = 16 ft³
- Dimensions: Length = 8 ft, Width = 2 ft, Height = ?
Using the volume formula:
Substitute the known values:
Solve for :
So, the missing dimension is 1 ft.
Would you like more details or explanations on any of these steps? Let me know if you have any questions! Here's a list of related questions:
- How do I calculate the volume of irregular shapes?
- What happens to the volume if one of the dimensions is doubled?
- How can the concept of volume be applied in real-life scenarios?
- How do you convert volume units (e.g., from cubic inches to cubic centimeters)?
- Can you find the volume of a cone using similar methods?
Tip: Always double-check the units for each dimension, as volume is very sensitive to the units used.
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Math Problem Analysis
Mathematical Concepts
Volume of Rectangular Prisms
Algebraic Manipulation
Solving for Missing Dimensions
Formulas
V = l × w × h
Theorems
Volume formula for rectangular prisms
Suitable Grade Level
Grades 6-8
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