This figure is not drawn to scale. A rectangular glass tank 80 cm by 55 cm by 50 cm has 2 compartments, C and D, with a water height of 33 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
= 36 x 33 x 55
= 65340 cm
3 Length of Compartment D
= 80 - 36
= 44 cm
Volume of the water in Compartment D
= 44 x 55 x 13
= 31460 cm
3 Total volume of water
= 65340 + 31460
= 96800 cm
3 Base area of the glass tank
= 80 x 55
= 4400 cm
2 Height of water
= 96800 ÷ 4400
= 22 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment C
= 33 - 22
= 11 cm
Drop in the volume of Compartment C
= 55 x 36 x 11
= 21780 cm
3 Volume of water flowed from C to D in 1 minute
= 21780 ÷ 75
≈ 290.4 cm
3 Answer(s): (a) 22 cm; (b) 290.4 cm
3