4. Applications of Derivatives
Differentials
Problem 4.6.57
Textbook Question
Approximating changes
Approximate the change in the volume of a right circular cylinder of fixed radius r = 20 cm when its height decreases from h = 12 to h = 11.9 cm (V(h) = πr²h).
Verified step by step guidance1
Identify the formula for the volume of a right circular cylinder, which is given by V(h) = πr²h, where r is the radius and h is the height.
Substitute the fixed radius r = 20 cm into the volume formula to express the volume in terms of height: V(h) = π(20)²h.
Calculate the initial volume V(12) when the height h = 12 cm by substituting h into the modified volume formula.
Calculate the new volume V(11.9) when the height h decreases to 11.9 cm by substituting this new height into the modified volume formula.
Find the approximate change in volume by subtracting the new volume V(11.9) from the initial volume V(12).
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