This figure is not drawn to scale. A rectangular glass tank 88 cm by 50 cm by 45 cm has 2 compartments, C and D, with a water height of 32 cm in C and 10 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 134 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
= 13 x 32 x 50
= 20800 cm
3 Length of Compartment D
= 88 - 13
= 75 cm
Volume of the water in Compartment D
= 75 x 50 x 10
= 37500 cm
3 Total volume of water
= 20800 + 37500
= 58300 cm
3 Base area of the glass tank
= 88 x 50
= 4400 cm
2 Height of water
= 58300 ÷ 4400
= 13.25 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment C
= 32 - 13.25
= 18.75 cm
Drop in the volume of Compartment C
= 50 x 13 x 18.75
= 12187.5 cm
3 Volume of water flowed from C to D in 1 minute
= 12187.5 ÷ 105
≈ 116.1 cm
3 Answer(s): (a) 13.25 cm; (b) 116.1 cm
3