A draining conical reservoir. Water is flowing at the rate of 50m^(3)//"min" from a shallow concrete conical reservoir (vertex down) of base radius 45 m and height 6 m. (a) How fast is the water level falling when the water is 5 m deep. (b) How fast is the radius of the water's surfce changing then ? Answer in cm/min.

A draining conical reservoir. Water is flowing at the rate of 50m^(3)/

1.	A draining conical reservoir. Water is flowing at the rate of 50m^(3)//"min" from a shallow concrete conical reservoir (vertex down) of base radius 45 m and height 6 m. (a) How fast is the water level falling when the water is 5 m deep. (b) How fast is the radius of the water's surfce changing then ? Answer in cm/min.
Answer» Solution :`(h)/(r)=(6)/(45)=(2)/(15)` `rArr " " (DH)/(dt)=(2)/(15) (DR)/(dt)` `h=5m rArr "" r=(15xx5)/(2)=(75)/(2)` `(DV)/(dt)=(pi)/(3)[2rh(dr)/(dt)+r^(2)(dh)/(dt)]` `rArr" " (150)/(pi)=75xx5 xx(dr)/(dt)((75)/(2))^(2)xx(2)/(15)(dr)/(dt)` `=(75xx5+(75xx75xx2)/(4xx15))(dr)/(dt)` `rArr " " (dr)/(dt)=(2xx150)/(3xx5xx75pi)=(4)/(15pi)m//"min"` `=(400)/(15pi)cm//"min"` `rArr " " (dh)/(dt)=(2)/(15)xx(400)/(15pi)=(800)/(225pi)cm//"min"`