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signokodo7h

Answered question

2021-11-06

Approximate the change in the volume of a right circular cylinder of fixed radius r=20 cm when its height decrees from h=12 cm to h=11.9 cm

(V (h) = π r^{2} h)

Steven Arredondo

Beginner2021-11-07Added 18 answers

To approximate the change in the volume of a right circular cylinder when its height decreases, we use the formula

△ y \approx f^{'} (a) △ x

The volume of the circular cylinder is

V (h) = π r^{2} h

with fixed radius
r=20cm. Therefore,

V (h) = 400 π h \Rightarrow V^{'} (h) = 400 π

Height decreases from 12 cm to 11.9 cm

\Rightarrow △ h = - 0.1

So the change in the volume when the height changes by

△ h

△ V \approx V^{'} (h) △ h

Substituting

V^{'} (h) = 400 π and △ h = - 0.1

, the approximate change in the volume is

△ V \approx 400 π △ h = - 40 π c m^{3}

Results:

V \approx - 40 π c m^{3}

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