This figure is not drawn to scale. A rectangular glass container 84 cm by 53 cm by 44 cm has 2 compartments, N and P, with a water height of 33 cm in N and 12 cm in P. A hole in the slider caused water to leak from N to P. 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 N to P in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment N
= 11 x 33 x 53
= 19239 cm
3 Length of Compartment P
= 84 - 11
= 73 cm
Volume of the water in Compartment P
= 73 x 53 x 12
= 46428 cm
3 Total volume of water
= 19239 + 46428
= 65667 cm
3 Base area of the glass container
= 84 x 53
= 4452 cm
2 Height of water
= 65667 ÷ 4452
= 14.75 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment N
= 33 - 14.75
= 18.25 cm
Drop in the volume of Compartment N
= 53 x 11 x 18.25
= 10639.75 cm
3 Volume of water flowed from N to P in 1 minute
= 10639.75 ÷ 72
≈ 147.8 cm
3 Answer(s): (a) 14.75 cm; (b) 147.8 cm
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