A spherical balloon is filled with 4500 ~ cubic meters of helium gas. If a leak in the balloon causes the gas to escape at the rate of 72 ~ cubic meters per minute then the rate (in meters per minute) at which the radius of the balloon decreases 49 ~min after the leakage began is
C. 2 9
V= 4 3 r^3 4500 = 4 r^3 3 r=15 ~m After 49 =(4500-49.72) =972 m ^3 aligned & & 972 & = 4 3 r^3 \\ & & r^3 & =3 243=3 3^5 aligned aligned r & =9 \\ d v d t & =4 r^2 ( d r d t ) \\ 72 & =4 9 9 ( d r d t ) \\ d r d t & = ( 2 9 ) aligned
Related: Mathematics — Application of Derivatives · All PYQ Banks