The Total solution for NCERT class 6-12
A balloon, which always remains spherical on inflation, isbeing inflated by pumping in 900 cubic centimetres of gas per second. Find therate at which the radius of the balloon increases when the radius is 15 cm.
The volume of a sphere (V) with radius (r)is given by,
∴Rate of change of volume (V) with respect to time (t) isgiven by,
[By chain rule]
It is given that
Therefore, when radius = 15 cm,
Hence, the rate at whichthe radius of the balloon increases when the radius is 15 cm is