This figure is not drawn to scale. A rectangular glass tank 90 cm by 50 cm by 49 cm has 2 compartments, K and L, with a water height of 32 cm in K and 14 cm in L. A hole in the slider caused water to leak from K to L. It was found that the water level in both compartments became the same after some time.
- What is the height of water in the tank now?
- It took 112 h for the water in both compartments to reach the same level. Assuming that water leaked at a constant rate, how much water flowed from K to L in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment K
= 13 x 32 x 50
= 20800 cm
3 Length of Compartment L
= 90 - 13
= 77 cm
Volume of the water in Compartment L
= 77 x 50 x 14
= 53900 cm
3 Total volume of water
= 20800 + 53900
= 74700 cm
3 Base area of the glass tank
= 90 x 50
= 4500 cm
2 Height of water
= 74700 ÷ 4500
= 16.6 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment K
= 32 - 16.6
= 15.4 cm
Drop in the volume of Compartment K
= 50 x 13 x 15.4
= 10010 cm
3 Volume of water flowed from K to L in 1 minute
= 10010 ÷ 90
≈ 111.2 cm
3 Answer(s): (a) 16.6 cm; (b) 111.2 cm
3