This figure is not drawn to scale. A rectangular glass container 80 cm by 55 cm by 46 cm has 2 compartments, Z and A, with a water height of 37 cm in Z and 15 cm in A. A hole in the slider caused water to leak from Z to A. 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 Z to A in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment Z
= 26 x 37 x 55
= 52910 cm
3 Length of Compartment A
= 80 - 26
= 54 cm
Volume of the water in Compartment A
= 54 x 55 x 15
= 44550 cm
3 Total volume of water
= 52910 + 44550
= 97460 cm
3 Base area of the glass container
= 80 x 55
= 4400 cm
2 Height of water
= 97460 ÷ 4400
= 22.15 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment Z
= 37 - 22.15
= 14.85 cm
Drop in the volume of Compartment Z
= 55 x 26 x 14.85
= 21235.5 cm
3 Volume of water flowed from Z to A in 1 minute
= 21235.5 ÷ 72
≈ 294.9 cm
3 Answer(s): (a) 22.15 cm; (b) 294.9 cm
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