This figure is not drawn to scale. A rectangular glass tank 80 cm by 51 cm by 47 cm has 2 compartments, R and S, with a water height of 34 cm in R and 10 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
= 39 x 34 x 51
= 67626 cm
3 Length of Compartment S
= 80 - 39
= 41 cm
Volume of the water in Compartment S
= 41 x 51 x 10
= 20910 cm
3 Total volume of water
= 67626 + 20910
= 88536 cm
3 Base area of the glass tank
= 80 x 51
= 4080 cm
2 Height of water
= 88536 ÷ 4080
= 21.7 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment R
= 34 - 21.7
= 12.3 cm
Drop in the volume of Compartment R
= 51 x 39 x 12.3
= 24464.7 cm
3 Volume of water flowed from R to S in 1 minute
= 24464.7 ÷ 105
≈ 233 cm
3 Answer(s): (a) 21.7 cm; (b) 233 cm
3