This figure is not drawn to scale. A rectangular glass tank 88 cm by 51 cm by 47 cm has 2 compartments, L and M, with a water height of 37 cm in L and 15 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 112 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
= 37 x 37 x 51
= 69819 cm
3 Length of Compartment M
= 88 - 37
= 51 cm
Volume of the water in Compartment M
= 51 x 51 x 15
= 39015 cm
3 Total volume of water
= 69819 + 39015
= 108834 cm
3 Base area of the glass tank
= 88 x 51
= 4488 cm
2 Height of water
= 108834 ÷ 4488
= 24.25 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment L
= 37 - 24.25
= 12.75 cm
Drop in the volume of Compartment L
= 51 x 37 x 12.75
= 24059.25 cm
3 Volume of water flowed from L to M in 1 minute
= 24059.25 ÷ 90
≈ 267.3 cm
3 Answer(s): (a) 24.25 cm; (b) 267.3 cm
3