This figure is not drawn to scale. A rectangular glass container 80 cm by 55 cm by 47 cm has 2 compartments, S and T, with a water height of 36 cm in S and 20 cm in T. A hole in the slider caused water to leak from S to T. It was found that the water level in both compartments became the same after some time.
- What is the height of water in the container 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 S to T in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment S
= 32 x 36 x 55
= 63360 cm
3 Length of Compartment T
= 80 - 32
= 48 cm
Volume of the water in Compartment T
= 48 x 55 x 20
= 52800 cm
3 Total volume of water
= 63360 + 52800
= 116160 cm
3 Base area of the glass container
= 80 x 55
= 4400 cm
2 Height of water
= 116160 ÷ 4400
= 26.4 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment S
= 36 - 26.4
= 9.6 cm
Drop in the volume of Compartment S
= 55 x 32 x 9.6
= 16896 cm
3 Volume of water flowed from S to T in 1 minute
= 16896 ÷ 105
≈ 160.9 cm
3 Answer(s): (a) 26.4 cm; (b) 160.9 cm
3