Math  /  Calculus

QuestionBack to Home Score: 3/5 Penalty: none
Related Rates Practice Due: November 25 at 7:30 AM Grade: 65\% \checkmark Related Rates - Rectangles \checkmark Related Rates - Triangles Related Rates (One Formula) Related Rates (Two Formulas)
Watch Video Show Examples Question \square \square The radius of a cylinder is decreasing at a constant rate of 10 inches per minute, and the volume is decreasing at a rate of 4698 cubic inches per minute. At the instant when the height of the cylinder is 5 inches and the volume is 1175 cubic inches, what is the rate of change of the height? The volume of a cylinder can be found with the equation V=πr2hV=\pi r^{2} h. Round your answer to three decimal places.
Answer Attempt 1 out of 4 \qquad inmin\frac{i n}{\min } Submit Answer

Studdy Solution
Compute the numerical value of dhdt \frac{dh}{dt} and round to three decimal places:
Calculate the expression:
dhdt4698+100π11755π11755π \frac{dh}{dt} \approx \frac{-4698 + 100\pi\sqrt{\frac{1175}{5\pi}}}{\frac{1175}{5\pi}}
After computation, round the result to three decimal places.
The rate of change of the height is approximately:
59.683 inches per minute \boxed{-59.683} \text{ inches per minute}

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