This figure is not drawn to scale. A rectangular glass tank 72 cm by 59 cm by 44 cm has 2 compartments, L and M, with a water height of 32 cm in L and 14 cm in M. A hole in the slider caused water to leak from L to M. 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 L to M in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment L
= 34 x 32 x 59
= 64192 cm
3 Length of Compartment M
= 72 - 34
= 38 cm
Volume of the water in Compartment M
= 38 x 59 x 14
= 31388 cm
3 Total volume of water
= 64192 + 31388
= 95580 cm
3 Base area of the glass tank
= 72 x 59
= 4248 cm
2 Height of water
= 95580 ÷ 4248
= 22.5 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment L
= 32 - 22.5
= 9.5 cm
Drop in the volume of Compartment L
= 59 x 34 x 9.5
= 19057 cm
3 Volume of water flowed from L to M in 1 minute
= 19057 ÷ 72
≈ 264.7 cm
3 Answer(s): (a) 22.5 cm; (b) 264.7 cm
3