This figure is not drawn to scale. A rectangular glass container 75 cm by 52 cm by 48 cm has 2 compartments, B and C, with a water height of 31 cm in B and 18 cm in C. A hole in the slider caused water to leak from B to C. 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 B to C in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment B
= 24 x 31 x 52
= 38688 cm
3 Length of Compartment C
= 75 - 24
= 51 cm
Volume of the water in Compartment C
= 51 x 52 x 18
= 47736 cm
3 Total volume of water
= 38688 + 47736
= 86424 cm
3 Base area of the glass container
= 75 x 52
= 3900 cm
2 Height of water
= 86424 ÷ 3900
= 22.16 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment B
= 31 - 22.16
= 8.84 cm
Drop in the volume of Compartment B
= 52 x 24 x 8.84
= 11032.32 cm
3 Volume of water flowed from B to C in 1 minute
= 11032.32 ÷ 105
≈ 105.1 cm
3 Answer(s): (a) 22.16 cm; (b) 105.1 cm
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