At any instant t, let r be the radius, V be the volume and S be the surface area of the balloon.
Given: dV/dt = 20cm
3/sec
As we know that, volume of sphere is given by:
πr3 where
r is the radius of the sphere.
i.e
V=πr3 Now differentiating V with respect to t we get
⇒=. ......(By chain Rule)
As,
V=πr3 ⇒=(πr3)=π.3r2 =4πr2 By substituting dV/dr in dV/dt we get
⇒=4πr2. Now substitute dV/dt = 20 cm
3/sec in the above equation we get
⇒20=4πr2.⇒= As we know that,
S=4πr2 By differentiating S with respect to t we get
⇒=. .....(By chain Rule)
⇒==8πr By substituting the value of dS/dr in dS/dt we get
⇒=8πr. By substituting
= in the above equation we get
⇒=8πr.= By substituting r = 8 cm in the above equation we get
⇒[]r=8==5cm2∕sec