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Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Topics In Analytic Geometry
Section: Chapter Questions
Problem 33CT
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The radius of a sphere is increasing at a rate of 3 mm/s. How fast is the volume increasing (in mm/s) when the diameter is 100 mm? (Round your answer to two decimal places.)
mm/s
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Please try again. Keep in mind that the volume of a sphere with radius r is V =
AĽ. Differentiate this equation with respect to time t using the Chain Rule to find the equation for the
rate at which the volume is increasing,
dv
Then, use the values from the exercise to evaluate the rate of change of the volume of the sphere, paying close attention to the signs of the
dt
rates of change (positive when increasing, and negative when decreasing). Have in mind that the diameter is twice the radius.
Transcribed Image Text:The radius of a sphere is increasing at a rate of 3 mm/s. How fast is the volume increasing (in mm/s) when the diameter is 100 mm? (Round your answer to two decimal places.) mm/s Enhanced Feedback Please try again. Keep in mind that the volume of a sphere with radius r is V = AĽ. Differentiate this equation with respect to time t using the Chain Rule to find the equation for the rate at which the volume is increasing, dv Then, use the values from the exercise to evaluate the rate of change of the volume of the sphere, paying close attention to the signs of the dt rates of change (positive when increasing, and negative when decreasing). Have in mind that the diameter is twice the radius.
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