This figure is not drawn to scale. A rectangular glass tank 85 cm by 50 cm by 50 cm has 2 compartments, C and D, with a water height of 33 cm in C and 19 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 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 C to D in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment C
= 34 x 33 x 50
= 56100 cm
3 Length of Compartment D
= 85 - 34
= 51 cm
Volume of the water in Compartment D
= 51 x 50 x 19
= 48450 cm
3 Total volume of water
= 56100 + 48450
= 104550 cm
3 Base area of the glass tank
= 85 x 50
= 4250 cm
2 Height of water
= 104550 ÷ 4250
= 24.6 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment C
= 33 - 24.6
= 8.4 cm
Drop in the volume of Compartment C
= 50 x 34 x 8.4
= 14280 cm
3 Volume of water flowed from C to D in 1 minute
= 14280 ÷ 90
≈ 158.7 cm
3 Answer(s): (a) 24.6 cm; (b) 158.7 cm
3