The length l, of a cylindrical balloon is in- creasing at a rate of 3 cm per second while the radius r, is increasing at 1 cm per second. Find the rate at which the volume is increas- ing when the length is 30 cm and the radius is 5 cm. The equation for the volume of this balloon is 4 V %3D
The length l, of a cylindrical balloon is in- creasing at a rate of 3 cm per second while the radius r, is increasing at 1 cm per second. Find the rate at which the volume is increas- ing when the length is 30 cm and the radius is 5 cm. The equation for the volume of this balloon is 4 V %3D
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...
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18
![**Problem 18:**
The length \( l \) of a cylindrical balloon is increasing at a rate of 3 cm per second while the radius \( r \) is increasing at 1 cm per second.
**Objective:** Find the rate at which the volume is increasing when the length is 30 cm and the radius is 5 cm.
**Volume Equation:** The equation for the volume \( V \) of this balloon is:
\[
V = \frac{4}{3} \pi r^3 + l \cdot \pi r^2
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffbc57344-aee0-4c7a-83a5-ce0e8c0e16d3%2F937a10b0-31a6-450d-ac15-eb820526e294%2F9n3z84_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 18:**
The length \( l \) of a cylindrical balloon is increasing at a rate of 3 cm per second while the radius \( r \) is increasing at 1 cm per second.
**Objective:** Find the rate at which the volume is increasing when the length is 30 cm and the radius is 5 cm.
**Volume Equation:** The equation for the volume \( V \) of this balloon is:
\[
V = \frac{4}{3} \pi r^3 + l \cdot \pi r^2
\]
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