Question
The rate of change of the area of a circle with respect to its radius $r$ at $r=6 \mathrm{~cm}$ is(A) $10 \pi$(B) $12 \pi$(C) $8 \pi$(D) $11 \pi$
Step 1
Step 1: The area $A$ of a circle with radius $r$ is given by the formula $A = \pi r^2$. Show more…
Show all steps
Your feedback will help us improve your experience
Tanishq Gupta and 66 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Find the rate of change of the area $A$ of a circle with respect to (a) the diameter $d ;$ (b) the circumference $C$.
The Derivative; The Process of Differentiation
The Derivative As A Rate of Change
Find the rate of change of the area of a circle with respect to its radius $r$ when (a) $r=3 \mathrm{~cm}$ (b) $r=4 \mathrm{~cm}$
Application of Derivatives
Introduction
A square of side length s is inscribed in a circle of radius r. (a) Write the area A of the square as a function of the radius r of the circle. (b) Find the (instantaneous) rate of change of the area A with respect to the radius r of the circle. (c) Evaluate the rate of change of $A$ at $r=1$ and $r=8$ (d) If $r$ is measured in inches and $A$ is measured in square inches, what units would be appropriate for $d A / d r ?$
Derivatives
Velocity and Other Rates of Change
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD