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The area of circle is given by A = pia r sq . where r is the radius . calculate the rate of increase of area w.r.t radius.?
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The area of circle is given by A = pia r sq . where r is the radius . ...
Rate of Increase of Area of Circle with respect to Radius
The area of a circle is given by the formula:
A = πr²
Deriving the Formula for Rate of Increase of Area
To find the rate of increase of area with respect to radius, we need to differentiate the area formula with respect to the radius:
dA/dt = d(πr²)/dr . dr/dt
Where:
- dA/dt is the rate of increase of area with respect to time
- dr/dt is the rate of increase of radius with respect to time
Using the power rule, we can differentiate the area formula:
dA/dr = 2πr
Substituting this into our initial formula, we get:
dA/dt = 2πr . dr/dt
Interpreting the Formula for Rate of Increase of Area
From the formula, we can see that the rate of increase of area is directly proportional to the radius and the rate of increase of the radius. This means that as the radius increases, the rate of increase of area also increases. Similarly, if the rate of increase of the radius increases, the rate of increase of area also increases.
It is important to note that the rate of increase of area is always greater than the rate of increase of the radius. This is because the area of a circle increases at a faster rate than its radius.
Conclusion
The formula for the rate of increase of area with respect to radius is:
dA/dt = 2πr . dr/dt
This formula shows us how the area of a circle changes as the radius changes. It is useful in many applications, such as in physics and engineering, where the area of a circle is an important parameter.
Community Answer
The area of circle is given by A = pia r sq . where r is the radius . ...
A=πr^2 dA/dr=d/dr(πr^2) =π*2r =2πr therefore,ans is 2πr.
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The area of circle is given by A = pia r sq . where r is the radius . calculate the rate of increase of area w.r.t radius.?
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The area of circle is given by A = pia r sq . where r is the radius . calculate the rate of increase of area w.r.t radius.? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about The area of circle is given by A = pia r sq . where r is the radius . calculate the rate of increase of area w.r.t radius.? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The area of circle is given by A = pia r sq . where r is the radius . calculate the rate of increase of area w.r.t radius.?.
The area of circle is given by A = pia r sq . where r is the radius . calculate the rate of increase of area w.r.t radius.? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about The area of circle is given by A = pia r sq . where r is the radius . calculate the rate of increase of area w.r.t radius.? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The area of circle is given by A = pia r sq . where r is the radius . calculate the rate of increase of area w.r.t radius.?.
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