A spherical balloon of radius r cm has volume Vcm^3 , where V =4/3 * pi * r^3. The balloon is inflated at a constant rate of 10 cm^3 s^-1 . Find the rate of increase of r when r = 8.

We are being asked to find the rate of change of radius, dr/dt. We will need to use the chain rule to do this: dV/dt = dV/dr * dr/dt.

We are given that dV/dt is 10cm^3 per second, and differentiating V = 4/3 * pi *r^3 with respect to r gives us dV/dr = 4 * pi *r^2 which at r= 8 gives us dV/dr = 804.25

Now rearranging the chain rule equation we find that dr/dt = (dV/dt) / (dV/dr) = 10/804.25 = 0.0124 cm per second.

MA
Answered by Max A. Maths tutor

12807 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

how do you differentiate y=x^2 from first principles?


The curve C has the equation: y=3x^2*(x+2)^6 Find dy/dx


A medical test will be positive for 0.05% of people and negative for everyone else. Suppose a hospital will test 4000 patients each day. Use an appropriate approximation to find the probability that 5 people test positive tomorrow. (5SF)


Find the intersection point of the line 2y=x+3 with the ellipse y^2+2x^2=3


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences