The radius of the tank is 10 m , and the rate of filling the tank is 314 cubic meter per hour .
Let the height of the cylindrical tank be h.
The volume of the tank is,
V=π× r 2 ×h =π ( 10 ) 2 h =100πh To find the rate of change of the volume, differentiate the above equation with respect to time.
dV dt =100π dh dt The tank is being filled by wheat at the rate of 314 cubic meter per hour . This is the rate of change of volume.
314=100π dh dt dh dt = 314 100×3.14 [ Take π=3.14 ] dh dt = 314 314 dh dt =1 Hence, the depth is increasing at a rate of 1 m/h .
Thus, the correct option is (A).