This figure is not drawn to scale. A rectangular glass tank 75 cm by 54 cm by 43 cm has 2 compartments, C and D, with a water height of 36 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 tank now?
- It took 114 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
= 21 x 36 x 54
= 40824 cm
3 Length of Compartment D
= 75 - 21
= 54 cm
Volume of the water in Compartment D
= 54 x 54 x 10
= 29160 cm
3 Total volume of water
= 40824 + 29160
= 69984 cm
3 Base area of the glass tank
= 75 x 54
= 4050 cm
2 Height of water
= 69984 ÷ 4050
= 17.28 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment C
= 36 - 17.28
= 18.72 cm
Drop in the volume of Compartment C
= 54 x 21 x 18.72
= 21228.48 cm
3 Volume of water flowed from C to D in 1 minute
= 21228.48 ÷ 75
≈ 283 cm
3 Answer(s): (a) 17.28 cm; (b) 283 cm
3