Question

The rate of change of volume of a sphere with respect to its surface area when the radius is $4cm$is

• A. $4c{m}^3/c{m}^2$
• B. $2c{m}^3/c{m}^2$
• C. $6c{m}^3/c{m}^2$
• D. $8c{m}^3/c{m}^2$

Answer 1

The correct option is B $2c{m}^3/c{m}^2$

$V=\frac{4}{3}\pi r^3\frac{dV}{dr}=4\pi r^{2}S=4\pi r^2\frac{dS}{dr}=8\pi r\frac{dV}{dS}=\frac{r}{2}=2c{m}^3/c{m}^2$