A water tank has the shape of an inverted right circular cone, whose semi-vertical angle is $\tan ^ { - 1 } \left( \frac { 1 } { 2 } \right)$. Water is poured into it at a constant rate of $5$ cubic $\mathrm { m } / \mathrm { min }$. Then the rate (in $\mathrm { m } / \mathrm { min }$), at which the level of water is rising at the instant when the depth of water in the tank is $10 m$; is: (1) $\frac { 1 } { 10 \pi }$ (2) $\frac { 1 } { 15 \pi }$ (3) $\frac { 1 } { 5 \pi }$ (4) $\frac { 2 } { \pi }$
A water tank has the shape of an inverted right circular cone, whose semi-vertical angle is $\tan ^ { - 1 } \left( \frac { 1 } { 2 } \right)$. Water is poured into it at a constant rate of $5$ cubic $\mathrm { m } / \mathrm { min }$. Then the rate (in $\mathrm { m } / \mathrm { min }$), at which the level of water is rising at the instant when the depth of water in the tank is $10 m$; is:\\
(1) $\frac { 1 } { 10 \pi }$\\
(2) $\frac { 1 } { 15 \pi }$\\
(3) $\frac { 1 } { 5 \pi }$\\
(4) $\frac { 2 } { \pi }$