This figure is not drawn to scale. A rectangular glass tank 78 cm by 51 cm by 44 cm has 2 compartments, R and S, with a water height of 39 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
= 26 x 39 x 51
= 51714 cm
3 Length of Compartment S
= 78 - 26
= 52 cm
Volume of the water in Compartment S
= 52 x 51 x 12
= 31824 cm
3 Total volume of water
= 51714 + 31824
= 83538 cm
3 Base area of the glass tank
= 78 x 51
= 3978 cm
2 Height of water
= 83538 ÷ 3978
= 21 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment R
= 39 - 21
= 18 cm
Drop in the volume of Compartment R
= 51 x 26 x 18
= 23868 cm
3 Volume of water flowed from R to S in 1 minute
= 23868 ÷ 105
≈ 227.3 cm
3 Answer(s): (a) 21 cm; (b) 227.3 cm
3