This figure is not drawn to scale. A rectangular glass tank 81 cm by 51 cm by 43 cm has 2 compartments, D and E, with a water height of 40 cm in D and 13 cm in E. A hole in the slider caused water to leak from D to E. 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 D to E in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment D
= 33 x 40 x 51
= 67320 cm
3 Length of Compartment E
= 81 - 33
= 48 cm
Volume of the water in Compartment E
= 48 x 51 x 13
= 31824 cm
3 Total volume of water
= 67320 + 31824
= 99144 cm
3 Base area of the glass tank
= 81 x 51
= 4131 cm
2 Height of water
= 99144 ÷ 4131
= 24 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment D
= 40 - 24
= 16 cm
Drop in the volume of Compartment D
= 51 x 33 x 16
= 26928 cm
3 Volume of water flowed from D to E in 1 minute
= 26928 ÷ 105
≈ 256.5 cm
3 Answer(s): (a) 24 cm; (b) 256.5 cm
3