Write a differential formula that estimates the given change in volume or surface area.
-The change in the surface area $S = 4 \pi r ^ { 2 }$ of a sphere when the radius changes from $r _ { 0 }$ to $r _ { 0 } + d x$
A) $\mathrm { dS } = 8 \pi \mathrm { r } _ { 0 } \mathrm { dr }$
B) $d S = 2 \pi r _ { 0 } d r$
C) $d S = 4 \pi r _ { 0 } ^ { 2 } d r$
D) $\mathrm { dS } = 4 \pi \mathrm { r } _ { 0 } \mathrm { dr }$

Question

Quizplus · Accepted Answer

The differential formula for the change in surface area of a sphere is obtained by differentiating the surface area formula $S = 4 \pi r^2$ with respect to $r$, giving $dS = 8 \pi r dr$. When $r = r_0$, it becomes $dS = 8 \pi r_0 dr$.

Write a Differential Formula That Estimates the Given Change in Volume