Write a differential formula that estimates the given change in volume or surface area.
-The change in the volume $V = \pi r ^ { 2 } h$ of a right circular cylinder when the height changes from $h _ { 0 }$ to $h _ { 0 } +$ dh and $^ { 2 }$ the radius does not change
A) $d V = \pi r ^ { 2 } h 0 d h$
B) $\mathrm { dV } = \pi \mathrm { r } _ { 0 } ^ { 2 } \mathrm { dr }$
C) $\mathrm { dV } = 2 \pi \mathrm { rh } 0 \mathrm { dh }$
D) $\mathrm { dV } = \pi \mathrm { r } ^ { 2 } \mathrm { dh }$

Question

Quizplus · Accepted Answer

The volume formula for a right circular cylinder is V = πr^2h. Differentiating this formula with respect to h gives dV/dh = πr^2. Therefore, when the height changes from h0 to h0 + dh and the radius remains constant, the change in volume can be estimated by dV=πr^2dh. This is option D.

Write a Differential Formula That Estimates the Given Change in Volume