Math Problem Statement
solve just simple working out
Solution
Let's solve each problem step-by-step.
Problem 7
We need to calculate the volume of the prism.
The prism's volume can be found using the formula:
Given:
- Area of cross-section = 42 m²
- Length (or height) = 8 m
Calculation:
Answer for Problem 7: The volume of the prism is 336 m³.
Problem 8
We need to find the volume of each prism by first calculating the area of the cross-section.
Problem 8a
Shape: Triangular Prism
Dimensions given:
- Base of triangle = 8 cm
- Height of triangle = 6 cm
- Length of prism = 10 cm
Steps:
-
Calculate the area of the triangle cross-section using the formula:
-
Calculate the volume of the prism using the formula:
Answer for Problem 8a: The volume of the prism is 240 cm³.
Problem 8b
Shape: Trapezoidal Prism
Dimensions given:
- Top base of trapezoid = 4 m
- Bottom base of trapezoid = 8 m
- Height of trapezoid = 5 m
- Length of prism = 12 m
Steps:
-
Calculate the area of the trapezoid cross-section using the formula:
-
Calculate the volume of the prism using the formula:
Answer for Problem 8b: The volume of the prism is 360 m³.
Would you like more details on any of these steps, or do you have any questions?
Related Questions:
- How do you find the area of a circle and use it to calculate the volume of a cylindrical prism?
- What is the formula for finding the surface area of a prism?
- How does the volume formula change for prisms with different cross-sectional shapes?
- Can you explain how to find the volume of a pyramid and how it differs from finding the volume of a prism?
- How would you calculate the volume of a prism with a polygonal cross-section like a pentagon or hexagon?
Tip: When calculating volumes, always ensure your cross-sectional area is correctly calculated based on the specific shape of the prism.
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Math Problem Analysis
Mathematical Concepts
Geometry
Prisms
Volumes
Formulas
Volume of a prism
Theorems
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Suitable Grade Level
Grades 5-7
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