This figure is not drawn to scale. A rectangular glass container 75 cm by 60 cm by 50 cm has 2 compartments, M and N, with a water height of 34 cm in M and 19 cm in N. A hole in the slider caused water to leak from M to N. 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 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 M to N in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment M
= 29 x 34 x 60
= 59160 cm
3 Length of Compartment N
= 75 - 29
= 46 cm
Volume of the water in Compartment N
= 46 x 60 x 19
= 52440 cm
3 Total volume of water
= 59160 + 52440
= 111600 cm
3 Base area of the glass container
= 75 x 60
= 4500 cm
2 Height of water
= 111600 ÷ 4500
= 24.8 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment M
= 34 - 24.8
= 9.2 cm
Drop in the volume of Compartment M
= 60 x 29 x 9.2
= 16008 cm
3 Volume of water flowed from M to N in 1 minute
= 16008 ÷ 105
≈ 152.5 cm
3 Answer(s): (a) 24.8 cm; (b) 152.5 cm
3