Question -
Answer -
Let the rate of change of the volume of theballoon be┬аk┬а(where┬аk┬аis a constant).
Integratingboth sides, we get:
тЗТ 4╧А ├Ч 33┬а= 3 (k┬а├Ч 0 +C)
тЗТ 108╧А = 3C
тЗТ C = 36╧А
At┬аt┬а= 3,┬аr┬а=6:
тЗТ 4╧А ├Ч 63┬а= 3 (k┬а├Ч3 + C)
тЗТ 864╧А = 3 (3k┬а+36╧А)
тЗТ 3k┬а= тАУ288╧А тАУ 36╧А= 252╧А
тЗТ┬аk┬а= 84╧А
Substituting the values of┬аk┬аandC in equation (1), we get:
Thus,the radius of the balloon after┬аt┬аseconds is
.