Get Answers to all your Questions

header-bg qa

13) A balloon, which always remains spherical, has a variable diameter \frac{3}{2}( 2x +1) Find the rate of change of its volume with respect to x.

Answers (1)

best_answer

Volume of sphere(V) = \frac{4}{3}\pi r^{3}
Diameter = \frac{3}{2}(2x+1)
So, radius(r) = \frac{3}{4}(2x+1)
\frac{dV}{dx} = \frac{d(\frac{4}{3}\pi r^{3})}{dx} = \frac{d(\frac{4}{3}\pi (\frac{3}{4}(2x+1))^{3})}{dx} = \frac{4}{3}\pi\times 3\times\frac{27}{64}(2x+1)^{2}\times 2
                                                                               = \frac{27}{8}\pi (2x+1)^{2}

Posted by

Gautam harsolia

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads