This figure is not drawn to scale. A rectangular glass container 90 cm by 59 cm by 41 cm has 2 compartments, Q and R, with a water height of 40 cm in Q and 19 cm in R. A hole in the slider caused water to leak from Q to R. 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 112 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 Q to R in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment Q
= 27 x 40 x 59
= 63720 cm
3 Length of Compartment R
= 90 - 27
= 63 cm
Volume of the water in Compartment R
= 63 x 59 x 19
= 70623 cm
3 Total volume of water
= 63720 + 70623
= 134343 cm
3 Base area of the glass container
= 90 x 59
= 5310 cm
2 Height of water
= 134343 ÷ 5310
= 25.3 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment Q
= 40 - 25.3
= 14.7 cm
Drop in the volume of Compartment Q
= 59 x 27 x 14.7
= 23417.1 cm
3 Volume of water flowed from Q to R in 1 minute
= 23417.1 ÷ 90
≈ 260.2 cm
3 Answer(s): (a) 25.3 cm; (b) 260.2 cm
3