This figure is not drawn to scale. A rectangular glass tank 84 cm by 56 cm by 42 cm has 2 compartments, R and S, with a water height of 33 cm in R and 12 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
= 40 x 33 x 56
= 73920 cm
3 Length of Compartment S
= 84 - 40
= 44 cm
Volume of the water in Compartment S
= 44 x 56 x 12
= 29568 cm
3 Total volume of water
= 73920 + 29568
= 103488 cm
3 Base area of the glass tank
= 84 x 56
= 4704 cm
2 Height of water
= 103488 ÷ 4704
= 22 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment R
= 33 - 22
= 11 cm
Drop in the volume of Compartment R
= 56 x 40 x 11
= 24640 cm
3 Volume of water flowed from R to S in 1 minute
= 24640 ÷ 105
≈ 234.7 cm
3 Answer(s): (a) 22 cm; (b) 234.7 cm
3