This figure is not drawn to scale. A rectangular glass tank 76 cm by 51 cm by 43 cm has 2 compartments, K and L, with a water height of 37 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
= 30 x 37 x 51
= 56610 cm
3 Length of Compartment L
= 76 - 30
= 46 cm
Volume of the water in Compartment L
= 46 x 51 x 18
= 42228 cm
3 Total volume of water
= 56610 + 42228
= 98838 cm
3 Base area of the glass tank
= 76 x 51
= 3876 cm
2 Height of water
= 98838 ÷ 3876
= 25.5 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment K
= 37 - 25.5
= 11.5 cm
Drop in the volume of Compartment K
= 51 x 30 x 11.5
= 17595 cm
3 Volume of water flowed from K to L in 1 minute
= 17595 ÷ 72
≈ 244.4 cm
3 Answer(s): (a) 25.5 cm; (b) 244.4 cm
3