R A region is bounded by two concentric circles, as shown by the shaded region in the figure above. The radius of the outer circle, R, is increasing at a constant rate of 2 inches per second. The radius of the inner circle, r, is decreasing at a constant rate of 1 inch per second. What is the rate of change, in square inches per second, of the area of the region at the instant when R is 4 inches and r is 3 inches? (A) 3π (B) 6π (C) 10T (D) 22π

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Question
R
A region is bounded by two concentric circles, as shown by the shaded region in the figure above. The radius of the
outer circle, R, is increasing at a constant rate of 2 inches per second. The radius of the inner circle, r, is decreasing
at a constant rate of 1 inch per second. What is the rate of change, in square inches per second, of the area of the
region at the instant when R is 4 inches and r is 3 inches?
(A) 3π
(B) 6π
(C) 10T
(D) 22π
Transcribed Image Text:R A region is bounded by two concentric circles, as shown by the shaded region in the figure above. The radius of the outer circle, R, is increasing at a constant rate of 2 inches per second. The radius of the inner circle, r, is decreasing at a constant rate of 1 inch per second. What is the rate of change, in square inches per second, of the area of the region at the instant when R is 4 inches and r is 3 inches? (A) 3π (B) 6π (C) 10T (D) 22π
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