Approximate the change in the volume of a right circular cylinder of fixed radius r=20cm...?

Question

when its height decreases from h=12cm to h=11.9cm (V(h)=(pi)r^2h)

Answer 1

The radius of the circular cylinder r = 20 cm

Initial height h_i = 20 cm

Final height h_f = 11.9 cm

The volume of the circular cylinder V = π r² h

The change in volume ΔV = V_f - V_i = π r² h_f - π r² h_i - = π r² (h_f - h_i)

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

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

Solution : The change in volume is - 40π

Comments

this isn't helpful though. you found the exact value, you didn't estimate using calculus

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Find the following answer using concept of calculus.

Answer 2

The fixed radius of the right circular cylinder is .

The height decreases from to .

Therefore, .

The change in height is .

The volume of the right circular cylinder is .

Apply derivative on each side.

.

Here and .

Substitute .

.

Here negative sign indicates decrease in volume.

The change in volume is .