This figure is not drawn to scale. A rectangular glass tank 80 cm by 54 cm by 46 cm has 2 compartments, K and L, with a water height of 34 cm in K and 18 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 115 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
= 38 x 34 x 54
= 69768 cm
3 Length of Compartment L
= 80 - 38
= 42 cm
Volume of the water in Compartment L
= 42 x 54 x 18
= 40824 cm
3 Total volume of water
= 69768 + 40824
= 110592 cm
3 Base area of the glass tank
= 80 x 54
= 4320 cm
2 Height of water
= 110592 ÷ 4320
= 25.6 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment K
= 34 - 25.6
= 8.4 cm
Drop in the volume of Compartment K
= 54 x 38 x 8.4
= 17236.8 cm
3 Volume of water flowed from K to L in 1 minute
= 17236.8 ÷ 72
≈ 239.4 cm
3 Answer(s): (a) 25.6 cm; (b) 239.4 cm
3