The rate of change of volume of a sphere with respect to its surface area when its radius is 6 m, is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 3 m3/m2
Both the volume and the surface area depend on r:
\( \displaystyle V=\frac{4}{3}\pi r^{3} \)
\( \displaystyle S=4\pi r^{2} \)
By the chain rule:
\( \displaystyle \frac{dV}{dS}=\frac{dV/dr}{dS/dr} \)
\( \displaystyle =\frac{4\pi r^{2}}{8\pi r} \)
\( \displaystyle =\frac{r}{2} \)
At r = 6 m, this is 3 m3/m2.
CBSE Applied Mathematics (Class XII):
Related Rates
