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The volume of water in a cylindrical tank is given by: V = r²h where V is the volume of water in m³, r is the radius of the tank in metres, and h is the height of the water in metres. For a certain tank, the radius is 3.0 m. This is a property of the tank, so it is a constant. Water is filling the tank, so the height and volume are constantly changin hence h and V are variables. At a certain point in time, the height of the tank is increasing by 0.21 metres/hour and the height is 29 metres. Determine the rate of change of volume (in units of m3/h) at this point in time. Give your answer to three decimal places. Hint 1: You are being asked to find dv/dt. Hint 2: dh/dt = 0.21 m/h

The volume of water in a cylindrical tank is given by: V = r²h where V is the volume of water in m³, r is the radius of the tank in metres, and h is the height of the water in metres. For a certain tank, the radius is 3.0 m. This is a property of the tank, so it is a constant. Water is filling the tank, so the height and volume are constantly changin hence h and V are variables. At a certain point in time, the height of the tank is increasing by 0.21 metres/hour and the height is 29 metres. Determine the rate of change of volume (in units of m3/h) at this point in time. Give your answer to three decimal places. Hint 1: You are being asked to find dv/dt. Hint 2: dh/dt = 0.21 m/h

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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The volume of water in a cylindrical tank is given by: V = лr²h where V is the volume of water in m³, r is the radius of the tank in metres, and h is the height of the water in metres. For a certain tank, the radius is 3.0 m. This is a property of the tank, so it is a constant. Water is filling the tank, so the height and volume are constantly changing hence h and V are variables. At a certain point in time, the height of the tank is increasing by 0.21 metres/hour and the height is 29 metres. Determine the rate of change of volume (in units of m³/h) at this point in time. Give your answer to three decimal places. Hint 1: You are being asked to find dv/dt. Hint 2: dh/dt = 0.21 m/h
Transcribed Image Text:The volume of water in a cylindrical tank is given by: V = лr²h where V is the volume of water in m³, r is the radius of the tank in metres, and h is the height of the water in metres. For a certain tank, the radius is 3.0 m. This is a property of the tank, so it is a constant. Water is filling the tank, so the height and volume are constantly changing hence h and V are variables. At a certain point in time, the height of the tank is increasing by 0.21 metres/hour and the height is 29 metres. Determine the rate of change of volume (in units of m³/h) at this point in time. Give your answer to three decimal places. Hint 1: You are being asked to find dv/dt. Hint 2: dh/dt = 0.21 m/h
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