Math Problem Statement
just answers please
A circle is growing, its radius increasing by 5 mm per second. Find the rate at which the area is changing at the moment when the radius is 22 mm.
Solution
To find the rate at which the area of the circle is changing () when the radius is 22 mm:
Formula:
The area of a circle is .
Differentiate with respect to :
Known values:
Calculation:
Using :
Final Answer:
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Math Problem Analysis
Mathematical Concepts
Calculus
Differentiation
Related Rates
Formulas
Area of a circle: A = πr²
Rate of change formula: dA/dt = 2πr(dr/dt)
Theorems
Derivative rules
Rate of change applications
Suitable Grade Level
Grade 11-12 or introductory college-level calculus
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