(a) Let the point on the ground below point A be O
so AO is the height of the water level before it overflows.
AO/x = sin 30
AO = (1/2)x cm
Hence height of water level just before it overflows is (1/2) x cm
(b) Triangle AFB is the base area of the water volume and height is x
AF/x = 2 cos 30 = 2 (√3/2) = √3
So AF = (√3)x
Area of AFB = (1/2)(√3 (x))(1/2)x = (√3/4) x2
Volume of water = (√3/4) x2 (x) = (√3/4) x3
x3 —-> 60s
(√3/4) x3 —–> 60 x (√3/4) = 25.98 ~ 26 seconds to the nearest seconds.
Hence time taken to fill the water to the height in (a) is ~ 26 seconds.