Saved Bookmarks
| 1. |
A spherical balloon is filled with 4500p cubic meters ofhelium gas. If a leak in the balloon causes the gas to escape at the rate of `72pi`cubic meters per minute, then the rate (in metersper minute) at which the radius of the balloon decreases 49 minutes after theleakage began is(1) `9/7`(2) `7/9`(3) `2/9`(4) `9/2` |
|
Answer» `V_i = 4500 pi m^3` `(d V_i)/(dt) = -72 pi m^3/(min)` `V_(49 min) = 4500 pi - (72 pi xx 49) = 4500 pi - 3528 pi` `= 972 pi m^3 ` `V= 4/3 pi r^3` at 49 min,`972 = 4/3 xx pi xx r^3` `r^3 = 3 xx 972/4` `r= 3^2 = 9 m` `(dv)/dt = 4/3 pi 3 r^2 (dr)/(dt)` `- 72 pi = 4/3 pi xx 3 xx 81 (dr)/(dt)` `(dr)/(dt) = -72/(4 xx 81) = -2/9` option 2 is correct |
|