This figure is not drawn to scale. A rectangular glass tank 90 cm by 51 cm by 41 cm has 2 compartments, R and S, with a water height of 36 cm in R and 18 cm in S. A hole in the slider caused water to leak from R to S. 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 R to S in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment R
= 29 x 36 x 51
= 53244 cm
3 Length of Compartment S
= 90 - 29
= 61 cm
Volume of the water in Compartment S
= 61 x 51 x 18
= 55998 cm
3 Total volume of water
= 53244 + 55998
= 109242 cm
3 Base area of the glass tank
= 90 x 51
= 4590 cm
2 Height of water
= 109242 ÷ 4590
= 23.8 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment R
= 36 - 23.8
= 12.2 cm
Drop in the volume of Compartment R
= 51 x 29 x 12.2
= 18043.8 cm
3 Volume of water flowed from R to S in 1 minute
= 18043.8 ÷ 105
≈ 171.8 cm
3 Answer(s): (a) 23.8 cm; (b) 171.8 cm
3