Approximating changes Approximate the change in the lateral surface area (excluding the area of the base) of a right circular cone of fixed height of ?h? = 6 m when its radius decreases from ?r =10 m to ?r? = 9.9 m S = ?r ? + h .2
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Solution 27E STEP 1 According to the approximation formula we can write f(x + x) f(x) = f(x).x f = f(x).x, Where f is the function,x is the variable and x is the change in x. STEP 2 Therefore according to this question, we have to approximate the change in the lateral surface area of a right circular cone of fixed height(h) and its radius(r) decreases from 10m to 9.9m. STEP 3 The lateral surface area of a right circular cone with radius r and height h is given by 2 2 S = r + h 2 2 r×2r 2 2 r (r +h +r) (2r +h ) S (r) = r + h + 2 2 = (r + h ) + 2 2 = 2 2 = 2 2 2r +h r +h r +h r +h Thus according to the equation ,we write S = S ().r......................(1) Here r=10 m and r = 9.9 10 = 0.1m Already given radius h=6m (1) (2r +h ) (2×10 +6 ) S = r = ( 0.1) = 236( 0.1) = 23.6m 3 r +h 10 +62 136 136 S = 23.6m3 136 23.6 3 Thus the change in S , S = 136m
Textbook: Calculus: Early Transcendentals
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
This full solution covers the following key subjects: area, decreases, approximate, base, change. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. Since the solution to 27E from 4.5 chapter was answered, more than 404 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 27E from chapter: 4.5 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. The answer to “Approximating changes Approximate the change in the lateral surface area (excluding the area of the base) of a right circular cone of fixed height of ?h? = 6 m when its radius decreases from ?r =10 m to ?r? = 9.9 m S = ?r ? + h .2” is broken down into a number of easy to follow steps, and 49 words.