Math Problem Statement
Fill in the missing numbers to complete the mapping for the given circle's radius and area.
Solution
The image shows a table where the radius of a circle is mapped to its area. The relationship between the radius and the area of a circle is given by the formula:
We are provided with areas in the form of multiples (like , , and ), and we need to find the corresponding radii , , and .
Solving for , , and :
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For area: So, .
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For area: So, .
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For area: So, .
Final values:
Would you like further details on the calculations or have any questions?
Here are 5 related questions to deepen understanding:
- What is the formula for the circumference of a circle?
- How would you calculate the radius if the area is given as ?
- What happens to the area if the radius of a circle is doubled?
- Can you find the diameter of the circle if the area is ?
- How is the area of a sector related to the total area of a circle?
Tip: Always check if units are consistent, especially when working with geometric shapes like circles. This ensures accurate calculations.
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Math Problem Analysis
Mathematical Concepts
Geometry
Area of a Circle
Radius
Formulas
Area of a circle A = πr^2
Theorems
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Suitable Grade Level
Grades 6-8