This figure is not drawn to scale. A rectangular glass container 75 cm by 52 cm by 50 cm has 2 compartments, C and D, with a water height of 31 cm in C and 10 cm in D. A hole in the slider caused water to leak from C to D. 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 C to D in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment C
= 37 x 31 x 52
= 59644 cm
3 Length of Compartment D
= 75 - 37
= 38 cm
Volume of the water in Compartment D
= 38 x 52 x 10
= 19760 cm
3 Total volume of water
= 59644 + 19760
= 79404 cm
3 Base area of the glass container
= 75 x 52
= 3900 cm
2 Height of water
= 79404 ÷ 3900
= 20.36 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment C
= 31 - 20.36
= 10.64 cm
Drop in the volume of Compartment C
= 52 x 37 x 10.64
= 20471.36 cm
3 Volume of water flowed from C to D in 1 minute
= 20471.36 ÷ 72
≈ 284.3 cm
3 Answer(s): (a) 20.36 cm; (b) 284.3 cm
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