This figure is not drawn to scale. A rectangular glass tank 84 cm by 58 cm by 41 cm has 2 compartments, C and D, with a water height of 33 cm in C and 12 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 115 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
= 26 x 33 x 58
= 49764 cm
3 Length of Compartment D
= 84 - 26
= 58 cm
Volume of the water in Compartment D
= 58 x 58 x 12
= 40368 cm
3 Total volume of water
= 49764 + 40368
= 90132 cm
3 Base area of the glass tank
= 84 x 58
= 4872 cm
2 Height of water
= 90132 ÷ 4872
= 18.5 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment C
= 33 - 18.5
= 14.5 cm
Drop in the volume of Compartment C
= 58 x 26 x 14.5
= 21866 cm
3 Volume of water flowed from C to D in 1 minute
= 21866 ÷ 72
≈ 303.7 cm
3 Answer(s): (a) 18.5 cm; (b) 303.7 cm
3