This figure is not drawn to scale. A rectangular glass tank 72 cm by 58 cm by 48 cm has 2 compartments, P and Q, with a water height of 35 cm in P and 11 cm in Q. A hole in the slider caused water to leak from P to Q. 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 P to Q in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment P
= 15 x 35 x 58
= 30450 cm
3 Length of Compartment Q
= 72 - 15
= 57 cm
Volume of the water in Compartment Q
= 57 x 58 x 11
= 36366 cm
3 Total volume of water
= 30450 + 36366
= 66816 cm
3 Base area of the glass tank
= 72 x 58
= 4176 cm
2 Height of water
= 66816 ÷ 4176
= 16 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment P
= 35 - 16
= 19 cm
Drop in the volume of Compartment P
= 58 x 15 x 19
= 16530 cm
3 Volume of water flowed from P to Q in 1 minute
= 16530 ÷ 75
≈ 220.4 cm
3 Answer(s): (a) 16 cm; (b) 220.4 cm
3