This figure is not drawn to scale. A rectangular glass tank 75 cm by 51 cm by 49 cm has 2 compartments, B and C, with a water height of 40 cm in B and 10 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 tank 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
= 38 x 40 x 51
= 77520 cm
3 Length of Compartment C
= 75 - 38
= 37 cm
Volume of the water in Compartment C
= 37 x 51 x 10
= 18870 cm
3 Total volume of water
= 77520 + 18870
= 96390 cm
3 Base area of the glass tank
= 75 x 51
= 3825 cm
2 Height of water
= 96390 ÷ 3825
= 25.2 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment B
= 40 - 25.2
= 14.8 cm
Drop in the volume of Compartment B
= 51 x 38 x 14.8
= 28682.4 cm
3 Volume of water flowed from B to C in 1 minute
= 28682.4 ÷ 105
≈ 273.2 cm
3 Answer(s): (a) 25.2 cm; (b) 273.2 cm
3