This figure is not drawn to scale. A rectangular glass tank 70 cm by 55 cm by 42 cm has 2 compartments, J and K, with a water height of 38 cm in J and 10 cm in K. A hole in the slider caused water to leak from J to K. 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 134 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 J to K in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment J
= 28 x 38 x 55
= 58520 cm
3 Length of Compartment K
= 70 - 28
= 42 cm
Volume of the water in Compartment K
= 42 x 55 x 10
= 23100 cm
3 Total volume of water
= 58520 + 23100
= 81620 cm
3 Base area of the glass tank
= 70 x 55
= 3850 cm
2 Height of water
= 81620 ÷ 3850
= 21.2 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment J
= 38 - 21.2
= 16.8 cm
Drop in the volume of Compartment J
= 55 x 28 x 16.8
= 25872 cm
3 Volume of water flowed from J to K in 1 minute
= 25872 ÷ 105
≈ 246.4 cm
3 Answer(s): (a) 21.2 cm; (b) 246.4 cm
3