Question

S=4*pi*(r^2) and V=(4*pi*(r^3))/3
find dS/dV

Answer 1

\[S=4\pi r^2\qquad\frac{\text dS}{\text dr}=8\pi r\]
\[V=\frac{ 4 \pi r^3}3\qquad\frac{\text dV}{\text dr}=4\pi r^2\]

\[\frac{\text dS}{\text dV}=\frac{\text dS}{\text dr}\cdot\frac{\text dr}{\text dV}=8\pi r\cdot\frac1{4\pi r^2}=\frac 2r\]

Answer 2

S=4*pi*(r^2) and V=(4*pi*(r^3))/3
a spherical balloon expands as air is pumped into it. what is the rate of increase in the balloon's surface area with volume when its volume is 30(cm^3)

Answer 3

solve for r,

plug r into dS/dV

Answer 4

can u pls solve it for me