This figure is not drawn to scale. A rectangular glass container 90 cm by 58 cm by 42 cm has 2 compartments, L and M, with a water height of 34 cm in L and 16 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 container 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
= 36 x 34 x 58
= 70992 cm
3 Length of Compartment M
= 90 - 36
= 54 cm
Volume of the water in Compartment M
= 54 x 58 x 16
= 50112 cm
3 Total volume of water
= 70992 + 50112
= 121104 cm
3 Base area of the glass container
= 90 x 58
= 5220 cm
2 Height of water
= 121104 ÷ 5220
= 23.2 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment L
= 34 - 23.2
= 10.8 cm
Drop in the volume of Compartment L
= 58 x 36 x 10.8
= 22550.4 cm
3 Volume of water flowed from L to M in 1 minute
= 22550.4 ÷ 72
≈ 313.2 cm
3 Answer(s): (a) 23.2 cm; (b) 313.2 cm
3