This figure is not drawn to scale. A rectangular glass container 90 cm by 59 cm by 44 cm has 2 compartments, C and D, with a water height of 36 cm in C and 17 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
= 36 x 36 x 59
= 76464 cm
3 Length of Compartment D
= 90 - 36
= 54 cm
Volume of the water in Compartment D
= 54 x 59 x 17
= 54162 cm
3 Total volume of water
= 76464 + 54162
= 130626 cm
3 Base area of the glass container
= 90 x 59
= 5310 cm
2 Height of water
= 130626 ÷ 5310
= 24.6 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment C
= 36 - 24.6
= 11.4 cm
Drop in the volume of Compartment C
= 59 x 36 x 11.4
= 24213.6 cm
3 Volume of water flowed from C to D in 1 minute
= 24213.6 ÷ 72
≈ 336.3 cm
3 Answer(s): (a) 24.6 cm; (b) 336.3 cm
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