This figure is not drawn to scale. A rectangular glass tank 70 cm by 50 cm by 42 cm has 2 compartments, B and C, with a water height of 38 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 112 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
= 32 x 38 x 50
= 60800 cm
3 Length of Compartment C
= 70 - 32
= 38 cm
Volume of the water in Compartment C
= 38 x 50 x 10
= 19000 cm
3 Total volume of water
= 60800 + 19000
= 79800 cm
3 Base area of the glass tank
= 70 x 50
= 3500 cm
2 Height of water
= 79800 ÷ 3500
= 22.8 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment B
= 38 - 22.8
= 15.2 cm
Drop in the volume of Compartment B
= 50 x 32 x 15.2
= 24320 cm
3 Volume of water flowed from B to C in 1 minute
= 24320 ÷ 90
≈ 270.2 cm
3 Answer(s): (a) 22.8 cm; (b) 270.2 cm
3