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Approximate the adjust in the volume that a appropriate circular cylinder of fixed radius r=20cm...? 0 votes

when its elevation decreases native h=12cm come h=11.9cm (V(h)=(pi)r^2h)

average-rate-of-changeaskedNov 15, 2014in PRECALCULUSby anonymousplease log in or register to include a comment. please log in or register to answer this question. 2 answer 0 votes

The radius of the circular cylinder r = 20 cm

Initial elevation hi = 20 cm

Final elevation hf = 11.9 cm

The volume that the one cylinder V = π r² h

The adjust in volume ΔV = Vf - using = π r² hf - π r² hello - = π r² (hf - hi)

ΔV = π (20)² (11.9 - 20) = 400 π (- 0.1) = - 40π

(The negative sign suggests that diminish of volume due to decreasing of height)

**Solution : The change in volume is - 40π**

Find the complying with answer using concept of calculus.

You are watching: Approximate the change in the volume of a right circular cylinder of fixed radius

The solved radius the the ideal circular cylinder is

.The height decreases from

come .Therefore,

.The readjust in elevation is

.The volume of the right circular cylinder is

.Apply derivative on each side.

.Here

and .Substitute

..Here negative sign shows decrease in volume.

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The change in volume is

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