This figure is not drawn to scale. A rectangular glass tank 75 cm by 53 cm by 49 cm has 2 compartments, C and D, with a water height of 35 cm in C and 13 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
= 24 x 35 x 53
= 44520 cm
3 Length of Compartment D
= 75 - 24
= 51 cm
Volume of the water in Compartment D
= 51 x 53 x 13
= 35139 cm
3 Total volume of water
= 44520 + 35139
= 79659 cm
3 Base area of the glass tank
= 75 x 53
= 3975 cm
2 Height of water
= 79659 ÷ 3975
= 20.04 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment C
= 35 - 20.04
= 14.96 cm
Drop in the volume of Compartment C
= 53 x 24 x 14.96
= 19029.12 cm
3 Volume of water flowed from C to D in 1 minute
= 19029.12 ÷ 75
≈ 253.7 cm
3 Answer(s): (a) 20.04 cm; (b) 253.7 cm
3