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Sand falls from a hopper at a rate of 0.5 cubic meters per hour and forms a conical pile beneath. Suppose the radius of the cone is always half the height of the cone. (a) Find the rate at which the radius of the cone increases when the radius is 2 meters. Give an exact answer. 0.5 8π meters per hour (b) Find the rate at which the height of the cone increases when the radius is 2 meters. Give an exact answer. 3 40T meters per hour

Sand falls from a hopper at a rate of 0.5 cubic meters per hour and forms a conical pile beneath. Suppose the radius of the cone is always half the height of the cone. (a) Find the rate at which the radius of the cone increases when the radius is 2 meters. Give an exact answer. 0.5 8π meters per hour (b) Find the rate at which the height of the cone increases when the radius is 2 meters. Give an exact answer. 3 40T meters per hour

Calculus: Early Transcendentals
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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Sand falls from a hopper at a rate of **0.5 cubic meters per hour** and forms a conical pile beneath. Suppose the radius of the cone is always half the height of the cone. ### (a) Find the rate at which the radius of the cone increases when the radius is **2 meters**. Give an exact answer. - Answer: \(\frac{0.5}{8\pi}\) - Unit: meters per hour - Status: Correct ✔️ ### (b) Find the rate at which the height of the cone increases when the radius is **2 meters**. Give an exact answer. - Answer: \(\frac{3}{40\pi}\) - Unit: meters per hour - Status: Incorrect ❌
Transcribed Image Text:Sand falls from a hopper at a rate of **0.5 cubic meters per hour** and forms a conical pile beneath. Suppose the radius of the cone is always half the height of the cone. ### (a) Find the rate at which the radius of the cone increases when the radius is **2 meters**. Give an exact answer. - Answer: \(\frac{0.5}{8\pi}\) - Unit: meters per hour - Status: Correct ✔️ ### (b) Find the rate at which the height of the cone increases when the radius is **2 meters**. Give an exact answer. - Answer: \(\frac{3}{40\pi}\) - Unit: meters per hour - Status: Incorrect ❌
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